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Fundamentals of Thermodynamics

Richard E. Sonntag, Claus Borgnakke, Gordon J. Van Wylen

Chapter 12

Gas Mixtures - all with Video Answers

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Chapter Questions

00:11

Problem 1

Are the mass and mole fractions for a mixture ever the same?

Keshav Singh
Keshav Singh
Numerade Educator
01:28

Problem 2

For a mixture how many component concentrations are needed?

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
01:32

Problem 3

Are any of the properties $(P, T, v)$ for oxygen and nitrogen in air the same?

Bhumika Jayee
Bhumika Jayee
Numerade Educator
02:27

Problem 4

If oxygen is $21 \%$ by mole of air, what is the oxygen state $(P, T, v)$ in a room at $300 \mathrm{K}, 100$ $\mathrm{kPa},$ of total volume $60 \mathrm{m}^{3} ?$

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
04:27

Problem 5

A flow of oxygen and one of nitrogen, both 300 $\mathrm{K},$ are mixed to produce $1 \mathrm{kg} / \mathrm{s}$ air at $300 \mathrm{K}, 100$ kPa. What are the mass and volume flow rates of each line?

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
03:29

Problem 6

A flow of gas $A$ and a flow of gas $B$ are mixed in a 1: 1 mole ratio with same $T .$ What is the entropy generation per kmole flow out?

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
05:08

Problem 7

A rigid container has 1 kg argon at $300 \mathrm{K}$ and $\mathrm{kg}$ argon at $400 \mathrm{K}$ both at $150 \mathrm{kPa} .$ Now they are allowed to mix without any external heat transfer. What is final $T, P ?$ Is any $s$ generated?

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
05:58

Problem 8

A rigid container has $1 \mathrm{kg} \mathrm{CO}_{2}$ at $300 \mathrm{K}$ and $\mathrm{kg}$ argon at $400 \mathrm{K},$ both at $150 \mathrm{kPa}$. Now they are allowed to mix without any heat transfer. What is final $T, P ?$

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
02:29

Problem 9

A flow of 1 kg/s argon at 300 K and another flow of $1 \mathrm{kg} / \mathrm{s} \mathrm{CO}_{2}$ at $1600 \mathrm{K}$ both at $150 \mathrm{kPa}$ are mixed without any heat transfer. What is the exit $T, P ?$

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
06:26

Problem 10

What is the rate of entropy increase in Problem $12.9 ?$

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
02:05

Problem 11

If $I$ want to heat a flow of a 4 -component mixture from 300 to $310 \mathrm{K}$ at constant $P$, how many properties and which ones do I need to know to find the heat transfer?

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
01:47

Problem 12

For a gas mixture in a tank, are the partial pressures important?

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
01:53

Problem 13

What happens to relative and absolute humidity when moist air is heated?

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
02:04

Problem 14

I cool moist air; do I reach the dew first in a constant $P$ or constant $V$ process?

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
00:42

Problem 15

What happens to relative and absolute humidity when moist air is cooled?

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
03:34

Problem 16

If I have air at $100 \mathrm{kPa}$ and $(a)-10^{\circ} \mathrm{C},(b) 45^{\circ} \mathrm{C}$ and (c) $110^{\circ} \mathrm{C}$, what is the maximum absolute humidity I can have?

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
00:50

Problem 17

Can moist air below the freezing point, say $-5^{\circ} \mathrm{C},$ have a dew point?

Sheh Lit Chang
Sheh Lit Chang
University of Washington
03:41

Problem 18

Explain in words what the absolute and relative humidity expresses?

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
01:00

Problem 19

An adiabatic saturation process changes $\Phi, \omega$ and $T$. In which direction?

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
02:24

Problem 20

I want to bring air at $35^{\circ} \mathrm{C}, \Phi=40 \%,$ to a state of $25^{\circ} \mathrm{C}, \omega=0.01 .$ Do I need to add or subtract water?

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
03:41

Problem 21

A gas mixture at $120^{\circ} \mathrm{C}$ and $125 \mathrm{kPa}$ is $50 \% \mathrm{N}_{2}$
$30 \% \mathrm{H}_{2} \mathrm{O},$ and $20 \% \mathrm{O}_{2}$ on a mole basis. Find the mass fractions, the mixture gas constant, and the volume for 5 kg of mixture.

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
04:16

Problem 22

A mixture of $60 \% \mathrm{N}_{2}, 30 \%$ argon, and $10 \% \mathrm{O}_{2}$ on a mass basis is in a cylinder at $250 \mathrm{kPa}$ and $310 \mathrm{K}$ with a volume of $0.5 \mathrm{m}^{3} .$ Find the mole fractions and the mass of argon.

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
03:39

Problem 23

A mixture of $60 \% \mathrm{N}_{2}, 30 \% \mathrm{Ar},$ and $10 \% \mathrm{O}_{2}$ on a mole basis is in a cylinder at $250 \mathrm{kPa}$ and $310 \mathrm{K}$ with a volume of $0.5 \mathrm{m}^{3}$. Find the mass fractions and the mass of argon.

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
05:49

Problem 24

A new refrigerant $R-407$ is a mixture of $23 \%$ $\mathrm{R}-32,25 \% \mathrm{R}-125,$ and $52 \% \mathrm{R}-134 \mathrm{a}$ on a mass basis. Find the mole fractions, the mixture gas constant, and the mixture heat capacities for this new refrigerant.

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
03:59

Problem 25

A carbureted internal combustion engine is converted to run on methane gas (natural gas). The air-fuel ratio in the cylinder is to be 20 to 1 on a mass basis. How many moles of oxygen per mole of methane are there in the cylinder?

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
07:45

Problem 26

Weighing of masses gives a mixture at $60^{\circ} \mathrm{C}$ $225 \mathrm{kPa}$ with $0.5 \mathrm{kg} \mathrm{O}_{2}, 1.5 \mathrm{kg} \mathrm{N}_{2},$ and $0.5 \mathrm{kg}$ $\mathrm{CH}_{4} .$ Find the partial pressures of each component, the mixture specific volume (mass basis), mixture molecular weight, and the total volume.

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
03:44

Problem 27

A 2 -kg mixture of $25 \% \mathrm{N}_{2}, 50 \% \mathrm{O}_{2},$ and $25 \%$ $\mathrm{CO}_{2}$ by mass is at $150 \mathrm{kPa}$ and $300 \mathrm{K}$. Find the mixture gas constant and the total volume.

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
04:34

Problem 28

A $100 \mathrm{m}^{3}$ storage tank with fuel gases is at $20^{\circ} \mathrm{C}$ and $100 \mathrm{kPa}$ containing a mixture of acetylene $\mathrm{C}_{2} \mathrm{H}_{2},$ propane $\mathrm{C}_{3} \mathrm{H}_{8},$ and butane $\mathrm{C}_{4} \mathrm{H}_{10} .$ A test shows the partial pressure of the $\mathrm{C}_{2} \mathrm{H}_{2}$ is $15 \mathrm{kPa}$ and that of $\mathrm{C}_{3} \mathrm{H}_{8}$ is $65 \mathrm{kPa}$. How much mass is there of each component?

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
03:49

Problem 29

A pipe, of cross-sectional area $0.1 \mathrm{m}^{2},$ carries a flow of $75 \% \mathrm{O}_{2}$ and $25 \% \mathrm{N}_{2}$ by mole with a velocity of $25 \mathrm{m} / \mathrm{s}$ at $200 \mathrm{kPa}$ and $290 \mathrm{K} .$ To install and operate a mass flow meter, it is necessary to know the mixture density and the gas constant. What are they? What mass flow rate should the meter then show?

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
03:47

Problem 30

A new refrigerant $R-410 a$ is a mixture of $R-32$ and $\mathrm{R}-125$ in a 1: 1 mass ratio. What are the overall molecular weight, the gas constant, and the ratio of specific heats for such a mixture?

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
06:02

Problem 31

At a certain point in a coal gasification process, a sample of the gas is taken and stored in a $1 \mathrm{L}$ cylinder. An analysis of the mixture yields the following results:
$$\begin{array}{lllll}
\hline \text { Component } & \mathbf{H}_{2} & \mathrm{CO} & \mathrm{CO}_{2} & \mathrm{N}_{2} \\
\hline \text { Percent by mass } & 2 & 45 & 28 & 25 \\
\hline
\end{array}$$
Determine the mole fractions and total mass in the cylinder at $100 \mathrm{kPa}$ and $20^{\circ} \mathrm{C}$. How much heat must be transferred to heat the sample at constant volume from the initial state to $100^{\circ} \mathrm{C} ?$

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
02:44

Problem 32

The mixture in Problem 12.27 is heated to $500 \mathrm{K}$ with constant volume. Find the final pressure and the total heat transfer needed using Table A.5.

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
03:01

Problem 33

The mixture in problem 12.27 is heated up to $500 \mathrm{K}$ in a constant-pressure process. Find the final volume and the total heat transfer using Table A.S.

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
02:13

Problem 34

A pipe flows $1.5 \mathrm{kg} / \mathrm{s}$ of a mixture with mass fractions of $40 \% \mathrm{CO}_{2}$ and $60 \% \mathrm{N}_{2}$ at $400 \mathrm{kPa}$ and $300 \mathrm{K},$ shown in Fig. $\mathrm{P} 12.34 .$ Heating tape is wrapped around a section of pipe with insulation added, and $2 \mathrm{kW}$ of electrical power is heating the pipe flow. Find the mixture exit temperature.

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
01:40

Problem 35

A pipe flows $0.05 \mathrm{kmol} / \mathrm{s}$ of a mixture with mole fractions of $40 \% \mathrm{CO}_{2}$ and $60 \% \mathrm{N}_{2}$ at $400 \mathrm{kPa}$ $300 \mathrm{K} .$ Heating tape is wrapped around a section of pipe with insulation added, and $2 \mathrm{kW}$ electrical power is heating the pipe flow. Find the mixture exit temperature.

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
08:50

Problem 36

A rigid insulated vessel contains $12 \mathrm{kg}$ of oxygen at $200 \mathrm{kPa}$ and $280 \mathrm{K}$ separated by a membrane from $26 \mathrm{kg}$ of carbon dioxide at $400 \mathrm{kPa}$ and $360 \mathrm{K}$. The membrane is removed, and the mixture comes to a uniform state. Find the final temperature and pressure of the mixture.

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
03:22

Problem 37

A mixture of $40 \%$ water and $60 \%$ carbon dioxide by mass is heated from $400 \mathrm{K}$. to $1000 \mathrm{K}$ at a constant pressure of $120 \mathrm{kPa}$. Find the total change in enthalpy and entropy using Table A.5 values.

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
03:05

Problem 38

Do Problem 12.37 but with variable heat capacity using values from Table A.8.

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
03:10

Problem 39

An insulated gas turbine receives a mixture of $10 \% \mathrm{CO}_{2}, 10 \% \mathrm{H}_{2} \mathrm{O},$ and $80 \% \mathrm{N}_{2}$ on a mass basis at $1000 \mathrm{K}$ and $500 \mathrm{kPa}$. The inlet volume flow rate is $2 \mathrm{m}^{3} / \mathrm{s}$, and the exhaust is at $700 \mathrm{K}$ and 100 kPa. Find the power output in $\mathrm{kW}$ using constant specific heat from Table A.5 at $300 \mathrm{K}.$

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
04:14

Problem 40

Solve Problem 12.39 using values of enthalpy from Table A.8.

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
02:30

Problem 41

An insulated gas turbine receives a mixture of $10 \% \mathrm{CO}_{2}, 10 \% \mathrm{H}_{2} \mathrm{O},$ and $80 \% \mathrm{N}_{2}$ on a mole basis at $1000 \mathrm{K}, 500 \mathrm{kPa}$. The inlet volume flow rate is $2 \mathrm{m}^{3} / \mathrm{s},$ and the exhaust is at $700 \mathrm{K}, 100$ kPa. Find the power output in $\mathrm{k} \mathrm{W}$ using constant specific heat from A. 5 at $300 \mathrm{K}.$

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
03:06

Problem 42

Solve Problem 12.41 using values of enthalpy from Table A.9.

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
04:23

Problem 43

A piston/cylinder device contains $0.1 \mathrm{kg}$ of a mixture of $40 \%$ methane and $60 \%$ propane by mass at $300 \mathrm{K}$ and $100 \mathrm{kPa}$. The gas is now slowly compressed in an isothermal $(T=\mathrm{con}-$ stant process to a final pressure of $250 \mathrm{kPa}$ Show the process in a $P-V$ diagram and find both the work and heat transfer in the process.

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
06:53

Problem 44

Consider Problem 12.39 and find the value for the mixture heat capacity, mass basis, and the mixture ratio of specific heats, $k_{\text {mix }},$ both estimated at $850 \mathrm{K}$ from values (differences) of $h$ in Table A.8. With these values make an estimate for the reversible adiabatic exit temperature of the turbine at $100 \mathrm{kPa}.$

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
05:25

Problem 45

Consider Problem 12.41 and find the value for the mixture heat capacity, mole basis, and the mixture ratio of specific heats, $k_{\operatorname{mix}},$ both estimated at $850 \mathrm{K}$ from values (differences) of $h$ in Table A.9. With these values make an estimate for the reversible adiabatic exit temperature of the turbine at $100 \mathrm{kPa}.$

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
03:35

Problem 46

A mixture of $0.5 \mathrm{kg}$ of nitrogen and $0.5 \mathrm{kg}$ of oxygen is at $100 \mathrm{kPa}$ and $300 \mathrm{K}$ in a piston cylinder keeping constant pressure. Now $800 \mathrm{kJ}$ is added by heating. Find the final temperature and the increase in entropy of the mixture using Table A.5 values.

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
06:24

Problem 47

Repeat Problem $12.46,$ but solve using values from Table A.8.

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
02:43

Problem 48

New refrigerant $R-410 a$ is a mixture of $R-32$ and $\mathrm{R}-125$ in a 1: 1 mass ratio. A process brings 0.5 kg $\mathrm{R}-410 \mathrm{a}$ from $270 \mathrm{K}$ to $320 \mathrm{K}$ at a constant pressure of $250 \mathrm{kPa}$ in a piston cylinder. Find the work and heat transfer.

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
04:25

Problem 49

A piston cylinder contains $0.5 \mathrm{kg}$ of argon and $0.5 \mathrm{kg}$ of hydrogen at $300 \mathrm{K}$ and $100 \mathrm{kPa}$. The mixture is compressed in an adiabatic process to $400 \mathrm{kPa}$ by an external force on the piston. Find the final temperature, the work, and the heat transfer in the process.

Narayan Hari
Narayan Hari
Numerade Educator
04:44

Problem 51

Natural gas as a mixture of $75 \%$ methane and $25 \%$ ethane by mass is flowing to a compressor at $17^{\circ} \mathrm{C}$ and $100 \mathrm{kPa}$. The reversible adiabatic compressor brings the flow to $250 \mathrm{kPa}$. Find the exit temperature and the needed work per $\mathrm{kg}$ flow.

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
04:57

Problem 51

A mixture of 2 kg of oxygen and $2 \mathrm{kg}$ of argon is in an insulated piston-cylinder arrangement at $100 \mathrm{kPa}$ and $300 \mathrm{K} .$ The piston now compresses the mixture to half its initial volume. Find the final pressure, final temperature, and the piston work.

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
05:37

Problem 52

The substance R-410a (see Problem 12.48) is at $100 \mathrm{kPa}$ and $290 \mathrm{K} .$ It is now brought to $250 \mathrm{kPa}$ and $400 \mathrm{K}$ in a reversible polytropic process Find the change in specific volume, specific enthalpy, and specific entropy for the process.

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
05:42

Problem 53

Two insulated tanks $A$ and $B$ are connected by a valve, shown in Fig. P12.53. Tank $A$ has a volume of $1 \mathrm{m}^{3}$ and initially contains argon at 300 $\mathrm{kPa}$ and $10^{\circ} \mathrm{C} .$ Tank $B$ has a volume of $2 \mathrm{m}^{3}$ and initially contains ethane at $200 \mathrm{kPa}$ and $50^{\circ} \mathrm{C}$ The valve is opened and remains open until the resulting gas mixture comes to a uniform state. Determine the final pressure and temperature.

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
04:04

Problem 54

A compressor brings $R-410 \mathrm{a}$ (see Problem 12.48 from $-10^{\circ} \mathrm{C}$ and $125 \mathrm{kPa}$ up to $500 \mathrm{kPa}$ in an adiabatic reversible compression. Assume ideal-gas behavior and find the exit temperature and the specific work.

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
02:54

Problem 55

A mixture of $50 \%$ carbon dioxide and $50 \%$ water by mass is brought from $1500 \mathrm{K}$ and 1 MPa to $500 \mathrm{K}$ and $200 \mathrm{kPa}$ in a polytropic process through a steady-state device. Find the necessary heat transfer and work involved using values from Table A.S.

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
05:41

Problem 56

Solve problem 12.55 using specific heats $C_{p}=$ $\Delta h / \Delta T$ from Table $A .8$ at $1000 \mathrm{K}.$

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
08:22

Problem 57

A $50 / 50$ (by mass) gas mixture of methane $\mathrm{CH}_{4}$ and ethylene $C_{2} H_{4}$ is contained in a cylinder piston at the initial state of $480 \mathrm{kPa}, 330 \mathrm{K},$ and $1.05 \mathrm{m}^{3} .$ The piston is now moved, compressing the mixture in a reversible, polytropic process to the final state of $260 \mathrm{K}$ and $0.03 \mathrm{m}^{3}$. Calculate the final pressure, the polytropic exponent, the work and heat transfer, and entropy change for the mixture.

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
05:38

Problem 58

The gas mixture from Problem 12.31 is compressed in a reversible adiabatic process from the initial state in the sample cylinder to a volume of 0.2 L. Determine the final temperature of the mixture and the work done during the process.

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
03:27

Problem 59

A flow of $2 \mathrm{kg} / \mathrm{s}$ mixture of $50 \% \mathrm{CO}_{2}$ and $50 \%$ $\mathrm{O}_{2}$ by mass is heated in a constant-pressure heat exchanger from $400 \mathrm{K}$ to $1000 \mathrm{K}$ by a radiation source at $1400 \mathrm{K}$. Find the rate of heat transfer and the entropy generation in the process shown in Fig. P12.59.

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
07:06

Problem 60

Carbon dioxide gas at $320 \mathrm{K}$ is mixed with $\mathrm{ni}$ trogen at $280 \mathrm{K}$ in an insulated mixing chamber. Both flows are at $100 \mathrm{kPa}$, and the mass ratio of carbon dioxide to nitrogen is $2: 1 .$ Find the exit temperature and the total entropy generation per $\mathrm{kg}$ of the exit mixture.

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
07:56

Problem 61

Repeat Problem 12.60 with inlet temperatures of $1400 \mathrm{K}$ for the carbon dioxide and $300 \mathrm{K}$ for the nitrogen. First estimate the exit temperature with the specific heats from Table $A .5$ and use this to start iterations with values from Table A.8.

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
08:32

Problem 62

Carbon dioxide gas at $320 \mathrm{K}$ is mixed with $\mathrm{ni}$ trogen at $280 \mathrm{K}$ in an insulated mixing chamber. Both flows are coming in at $100 \mathrm{kPa}$ and the mole ratio of carbon dioxide to nitrogen is 2: 1 Find the exit temperature and the total entropy generation per kmole of the exit mixture.

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
08:34

Problem 63

Repeat Problem 12.62 with inlet temperature of $1400 \mathrm{K}$ for the carbon dioxide and $300 \mathrm{K}$ for the nitrogen. First estimate the exit temperature with the specific heats from Table $A .5$ and use this to start iterations with values from A.9.

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
08:18

Problem 64

The only known sources of helium are the atmosphere (mole fraction approximately $5 \times 10^{-6}$ ) and natural gas. A large unit is being constructed to separate $100 \mathrm{m}^{3} / \mathrm{s}$ of natural gas, assumed to be 0.001 He mole fraction and 0.999 $\mathrm{CH}_{4}$. The gas enters the unit at $150 \mathrm{kPa}, 10^{\circ} \mathrm{C}.$ Pure helium exits at $100 \mathrm{kPa}, 20^{\circ} \mathrm{C},$ and pure methane exits at $150 \mathrm{kPa}, 30^{\circ} \mathrm{C}$. Any heat transfer is with the surroundings at $20^{\circ} \mathrm{C}$. Is an electrical power input of $3000 \mathrm{kW}$ sufficient to drive this unit?

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
07:26

Problem 65

A flow of $1 \mathrm{kg} / \mathrm{s}$ carbon dioxide at $1600 \mathrm{K}, 100$ $\mathrm{kPa}$ is mixed with a flow of $2 \mathrm{kg} / \mathrm{s}$ water at 800 $\mathrm{K}, 100 \mathrm{kPa},$ and after the mixing it goes through a heat exchanger where it is cooled to $500 \mathrm{K}$ by a $400 \mathrm{K}$ ambient. How much heat transfer is taken out in the heat exchanger? What is the entropy generation rate for the whole process?

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
05:12

Problem 66

A mixture of $60 \%$ helium and $40 \%$ nitrogen by mass enters a turbine at $1 \mathrm{MPa}$ and $800 \mathrm{K}$ at a rate of $2 \mathrm{kg} / \mathrm{s}$. The adiabatic turbine has an exit pressure of $100 \mathrm{kPa}$ and an isentropic efficiency of $85 \% .$ Find the turbine work.

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
04:54

Problem 67

Repeat Problem 12.50 for an isentropic compressor efficiency of $82 \%.$

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
07:48

Problem 68

A large air separation plant takes in ambient air $\left(79 \% \mathrm{N}_{2}, 21 \% \mathrm{O}_{2} \text { by mole }\right)$ at $100 \mathrm{kPa}$ and $20^{\circ} \mathrm{C}$ at a rate of $25 \mathrm{kg} / \mathrm{s}$. It discharges a stream of pure $\mathrm{O}_{2}$ gas at $200 \mathrm{kPa}$ and $100^{\circ} \mathrm{C}$ and a stream of pure $\mathrm{N}_{2}$ gas at $100 \mathrm{kPa}$ and $20^{\circ} \mathrm{C}$. The plant operates on an electrical power input of 2000 $\mathrm{kW},$ shown in Fig. $\mathrm{P} 12.68 .$ Calculate the net rate of entropy change for the process.

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
07:12

Problem 69

A steady flow of $0.3 \mathrm{kg} / \mathrm{s}$ of $50 \%$ carbon dioxide and $50 \%$ water by mass at $1200 \mathrm{K}$ and $200 \mathrm{kPa}$ is used in a heat exchanger where $300 \mathrm{kW}$ is extracted from the flow. Find the flow exit temperature and the rate of change of entropy using Table A.8.

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
04:44

Problem 70

A steady flow of $0.01 \mathrm{kmol} / \mathrm{s}$ of $50 \%$ carbon dioxide and $50 \%$ water on a mole basis at 1200 $\mathrm{K}$ and $200 \mathrm{kPa}$ is used in a heat exchanger where $300 \mathrm{kW}$ is extracted from the flow. Find the flow exit temperature and the rate of change of entropy using Table A.9.

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
05:51

Problem 71

A flow of $1.8 \mathrm{kg} / \mathrm{s}$ steam at $400 \mathrm{kPa}, 400^{\circ} \mathrm{C},$ is
mixed with $3.2 \mathrm{kg} / \mathrm{s}$ oxygen at $400 \mathrm{kPa}, 400 \mathrm{K}$
in a steady flow mixing-chamber without any heat transfer. Find the exit temperature and the rate of entropy generation.

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
06:15

Problem 72

A tank has two sides initially separated by a diaphragm, shown in Fig. P12.72. Side $A$ contains $1 \mathrm{kg}$ of water and side $B$ contains $1.2 \mathrm{kg}$ of air, both at $20^{\circ} \mathrm{C}$ and 10.0 kPa. The diaphragm is now broken, and the whole tank is heated to $600^{\circ} \mathrm{C}$ by a $700^{\circ} \mathrm{C}$ reservoir. Find the final total pressure, heat transfer, and total en. tropy generation.

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
11:09

Problem 73

Three steady flows are mixed in an adiabatic chamber at $150 \mathrm{kPa}$. Flow one is $2 \mathrm{kg} / \mathrm{s}$ of $\mathrm{O}_{2}$ at $340 \mathrm{K},$ flow two is $4 \mathrm{kg} / \mathrm{s}$ of $\mathrm{N}_{2}$ at $280 \mathrm{K},$ and flow three is $3 \mathrm{kg} / \mathrm{s}$ of $\mathrm{CO}_{2}$ at $310 \mathrm{K}$. All flows are at $150 \mathrm{kPa}$, the same as the total exit pressure. Find the exit temperature and the rate of entropy generation in the process.

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
10:07

Problem 74

Reconsider Problem $12.53,$ but let the tanks have a small amount of heat transfer so the final mixture is at $400 \mathrm{K}$. Find the final pressure, the heat transfer, and the entropy change for the process.

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
02:06

Problem 75

Atmospheric air is at $100 \mathrm{kPa}$ and $25^{\circ} \mathrm{C}$ with a relative humidity of $75 \%$. Find the absolute humidity and the dew point of the mixture. If the mixture is heated to $30^{\circ} \mathrm{C}$, what is the new relative humidity?

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
03:42

Problem 76

Consider $100 \mathrm{m}^{3}$ of atmospheric air, which is an air- -water vapor mixture at $100 \mathrm{kPa}, 15^{\circ} \mathrm{C}$, and $40 \%$ relative humidity. Find the mass of water and the humidity ratio. What is the dew point of the mixture?

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
00:50

Problem 77

The products of combustion are flowing through a heat exchanger with $12 \% \mathrm{CO}_{2}, 13 \% \mathrm{H}_{2} \mathrm{O},$ and $75 \% \mathrm{N}_{2}$ on a volume basis at the rate $0.1 \mathrm{kg} / \mathrm{s}$ and $100 \mathrm{kPa}$. What is the dew-point temperature? If the mixture is cooled $10^{\circ} \mathrm{C}$ below the dew-point temperature, how long will it take to collect $10 \mathrm{kg}$ of liquid water?

Hast Aggarwal
Hast Aggarwal
Numerade Educator
03:37

Problem 78

A $1 \mathrm{kg} / \mathrm{s}$ flow of saturated moist air (relative humidity $100 \%$ at $100 \mathrm{kPa}$ and $10^{\circ} \mathrm{C}$ goes through a heat exchanger and comes out at $25^{\circ} \mathrm{C}$. What is the exit relative humidity and how much power is needed?

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
03:45

Problem 79

A new high-efficiency home heating system includes an air-to-air heat exchanger, which uses energy from outgoing stale air to heat the fresh incoming air. If the outside ambient temperature is $-10^{\circ} \mathrm{C}$ and the relative humidity is $30 \%,$ how much water will have to be added to the incoming air, if it flows in at the rate of $1 \mathrm{m}^{3} / \mathrm{s}$ and must eventually be conditioned to $20^{\circ} \mathrm{C}$ and $40 \%$ relative humidity?

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
04:12

Problem 80

Consider a $1 \mathrm{m}^{3} / \mathrm{s}$ flow of atmospheric air at 100 $\mathrm{kPa}, 25^{\circ} \mathrm{C},$ and $80 \%$ relative humidity. Assume this flows into a basement room where it cools to $15^{\circ} \mathrm{C}$ at $100 \mathrm{kPa}$. How much liquid water will condense out?

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
04:22

Problem 81

A 2 kg/s flow of completely dry air at $T_{1}$ and 100 $\mathrm{kPa}$ is cooled down to $10^{\circ} \mathrm{C}$ by spraying liquid water at $10^{\circ} \mathrm{C}$ and $100 \mathrm{kPa}$ into it so it becomes saturated moist air at $10^{\circ} \mathrm{C}$. The process is steady state with no external heat transfer or work. Find the exit moist air humidity ratio and the flow rate of liquid water. Find also the dry air inlet temperature $T_{1}.$

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
10:14

Problem 82

A piston cylinder has 100 kg of saturated moist air at $100 \mathrm{kPa}$ and $5^{\circ} \mathrm{C}$. If it is heated to $45^{\circ} \mathrm{C}$ in an isobaric process, find $_{1} q_{2}$ and the final relative humidity. If it is compressed from the initial state to $200 \mathrm{kPa}$ in an isothermal process, find the mass of water condensing.

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
07:01

Problem 83

A saturated air-water vapor mixture at $20^{\circ} \mathrm{C}$ $100 \mathrm{kPa},$ is contained in a $5-\mathrm{m}^{3}$ closed tank in equilibrium with $1 \mathrm{kg}$ of liquid water. The tank is heated to $80^{\circ} \mathrm{C}$. Is there any liquid water at the final state? Find the heat transfer for the process.

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
08:45

Problem 84

Ambient moist air enters a steady-flow airconditioning unit at $102 \mathrm{kPa}$ and $30^{\circ} \mathrm{C}$ with a $60 \%$ relative humidity. The volume flow rate entering the unit is 100 L/s. The moist air leaves the unit at $95 \mathrm{kPa}$ and $15^{\circ} \mathrm{C}$ with a relative humidity of $100 \% .$ Liquid condensate also leaves the unit at $15^{\circ} \mathrm{C}$. Determine the rate of heat transfer for this process.

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
06:33

Problem 85

Consider at $500 \mathrm{L}$ rigid tank containing an air-water vapor mixture at $100 \mathrm{kPa}$ and $35^{\circ} \mathrm{C}$ with a $70 \%$ relative humidity. The system is cooled until the water just begins to condense. Determine the final temperature in the tank and the heat transfer for the process.

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
10:11

Problem 86

Air in a piston cylinder is at $35^{\circ} \mathrm{C}, 100 \mathrm{kPa}$, and a relative humidity of $80 \% .$ It is now compressed to a pressure of $500 \mathrm{kPa}$ in a constanttemperature process. Find the final relative and specific humidity and the volume ratio $V_{2} / V_{1}.$

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
07:06

Problem 87

A 300 L rigid vessel initially contains moist air at $150 \mathrm{kPa}$ and $40^{\circ} \mathrm{C}$ with a relative humidity of $10 \% .$ A supply line connected to this vessel by a valve carries steam at $600 \mathrm{kPa}$ and $200^{\circ} \mathrm{C}$. The valve is opened, and steam flows into the vessel until the relative humidity of the resultant moist air mixture is $90 \%$. Then the valve is closed. Sufficient heat is transferred from the vessel so that the temperature remains at $40^{\circ} \mathrm{C}$ during the process. Determine the heat transfer for the process, the mass of steam entering the vessel, and the final pressure inside the vessel.

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
07:42

Problem 88

A rigid container, $10 \mathrm{m}^{3}$ in volume, contains moist air at $45^{\circ} \mathrm{C}$ and $100 \mathrm{kPa}$ with $\Phi=40 \%$ The container is now cooled to $5^{\circ} \mathrm{C}$. Neglect the volume of any liquid that might be present and find the final mass of water vapor, final total pressure, and the heat transfer.

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
01:11

Problem 89

A water-filled reactor of $1 \mathrm{m}^{3}$ is at $20 \mathrm{MPa}$ $360^{\circ} \mathrm{C}$ and is located inside an insulated containment room of $100 \mathrm{m}^{3}$ that contains air at 100 $\mathrm{kPa}$ and $25^{\circ} \mathrm{C} .$ Due to a failure, the reactor ruptures and the water fills the containment room. Find the final quality and pressure by iterations.

Hast Aggarwal
Hast Aggarwal
Numerade Educator
05:13

Problem 90

A flow of moist air at $100 \mathrm{kPa}, 40^{\circ} \mathrm{C},$ and $40 \%$ relative humidity is cooled to $15^{\circ} \mathrm{C}$ in a constant-pressure device. Find the humidity ratio of the inlet and the exit flow and the heat transfer in the device per kg dry air.

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
08:47

Problem 91

A flow, $0.2 \mathrm{kg} / \mathrm{s}$ dry air, of moist air at $40^{\circ} \mathrm{C}$ and $50 \%$ relative humidity fiows from the outside state 1 down into a basement where it cools to $16^{\circ} \mathrm{C},$ state $2 .$ Then it flows up to the living room where it is heated to $25^{\circ} \mathrm{C}$, state 3 . Find the dew point for state $1,$ any amount of liquid that may appear, the heat transfer that takes place in the basement, and the relative humidity in the living room at state 3.

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
11:46

Problem 92

Two moist air streams with $85 \%$ relative humidity, both flowing at a rate of $0.1 \mathrm{kg} / \mathrm{s}$ of dry air, are mixed in a steady-flow setup. One inlet stream is at $32.5^{\circ} \mathrm{C}$ and the other at $16^{\circ} \mathrm{C}$. Find the exit relative humidity.

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
02:02

Problem 93

The discharge moist air from a clothes dryer is at $35^{\circ} \mathrm{C}, 80 \%$ relative humidity. The flow is guided through a pipe up through the roof and a vent to the atmosphere shown in Fig. P12.93. Due to heat transfer in the pipe, the flow is cooled to $24^{\circ} \mathrm{C}$ by the time it reaches the vent. Find the humidity ratio in the flow out of the clothes dryer and at the vent. Find the heat transfer and any amount of liquid that may be forming per kg dry air for the flow.

Kratika Bhadauria
Kratika Bhadauria
Numerade Educator
05:50

Problem 94

A steady supply of $1.0 \mathrm{m}^{3} / \mathrm{s}$ air at $25^{\circ} \mathrm{C}, 100 \mathrm{kPa}$ and $50 \%$ relative humidity is needed to heat a building in the winter. The ambient outdoors is at $10^{\circ} \mathrm{C}, 100 \mathrm{kPa}$, and $50 \%$ relative humidity. What are the required liquid water input and heat transfer rates for this purpose?

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
08:03

Problem 95

A combination air cooler and dehumidification unit receives outside ambient air at $35^{\circ} \mathrm{C}, 100$ $\mathrm{kPa},$ and $90 \%$ relative humidity. The moist air is first cooled to a low temperature $T_{2}$ to condense the proper amount of water; assume all the liquid leaves at $T_{2}$. The moist air is then heated and leaves the unit at $20^{\circ} \mathrm{C}, 100 \mathrm{kPa}$, and $30 \%$ relative humidity with a volume flow rate of 0.01 $\mathrm{m}^{3} / \mathrm{s} .$ Find the temperature $T_{2},$ the mass of liquid per kilogram of dry air, and the overall heat transfer rate.

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
06:34

Problem 96

Use the formulas and the steam tables to find the missing property of: $\Phi, \omega,$ and $T_{\mathrm{dry}},$ for a total pressure of $100 \mathrm{kPa}$; repeat the answers using the psychrometric chart.
a. $\Phi=50 \%, \omega=0.010$.
b. $T_{\mathrm{dry}}^{\prime}=25^{\circ} \mathrm{C}, T_{\mathrm{wet}}=21^{\circ} \mathrm{C}$.

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
03:19

Problem 97

An insulated tank has an air inlet, $\omega_{1}=0.0084$ and an outlet, $T_{2}=22^{\circ} \mathrm{C}, \Phi_{2}=90 \%,$ both at 100 kPa. A third line sprays $0.25 \mathrm{kg} / \mathrm{s}$ of water at $80^{\circ} \mathrm{C}$ and $100 \mathrm{kPa}$, as shown in Fig. P12.97. For steady operation, find the outlet specific humidity, the mass flow rate of air needed, and the required air inlet temperature, $T_{1}.$

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
02:47

Problem 98

A flow of moist air from a domestic furnace, state $1,$ is at $45^{\circ} \mathrm{C}, 10 \%$ relative humidity with a flow rate of $0.05 \mathrm{kg} / \mathrm{s}$ dry air. A small electric heater adds steam at $100^{\circ} \mathrm{C}, 100 \mathrm{kPa}$, generated from tap water at $15^{\circ} \mathrm{C}$ shown in Fig. P12.98. Up in the living room, the flow comes out at state 4: $30^{\circ} \mathrm{C}, 60 \%$ relative humidity. Find the power needed for the electric heater and the heat transfer to the flow from state 1 to state 4.

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
02:11

Problem 99

A water-cooling tover for a power plant cools $45^{\circ} \mathrm{C}$ liquid water by evaporation. The tower receives air at $19.5^{\circ} \mathrm{C}, \Phi=30 \%,$ and $100 \mathrm{kPa}$ that is blown through/over the water such that it leaves the tower at $25^{\circ} \mathrm{C}$ and $\Phi=70 \% .$ The remaining liquid water flows back to the condenser at $30^{\circ} \mathrm{C}$ having given off $1 \mathrm{MW}$. Find the mass flow rate of air, and determine the amount of water that evaporates.

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
03:44

Problem 100

A flow of air at $5^{\circ} \mathrm{C}, \Phi=90 \%,$ is brought into a house, where it is conditioned to $25^{\circ} \mathrm{C}, 60 \%$ relative humidity. This is done with a combined heater-evaporator where any liquid water is at $10^{\circ} \mathrm{C} .$ Find any flow of liquid and the necessary heat transfer, both per kilogram dry air flowing. Find the dew point for the final mixture.

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
05:09

Problem 101

In a car's defrost/defog system atmospheric air at $21^{\circ} \mathrm{C}$ and $80 \%$ relative humidity is taken in and cooled such that liquid water drips out. The now dryer air is heated to $41^{\circ} \mathrm{C}$ and then blown onto the windshield, where it should have a maximum of $10 \%$ relative humidity to remove water from the windshield. Find the dew point of the atmospheric air, specific humidity of air onto the windshield, the lowest temperature, and the specific heat transfer in the cooler.

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
06:49

Problem 102

Atmospheric air at $35^{\circ} \mathrm{C}$ with a relative humidity of $10 \%,$ is too warm and also too dry. An air conditioner should deliver air at $21^{\circ} \mathrm{C}$ and $50 \%$ relative humidity in the amount of $3600 \mathrm{m}^{3} / \mathrm{h}$ Sketch a setup to accomplish this. Find any amount of liquid (at $20^{\circ} \mathrm{C}$ ) that is needed or discarded and any heat transfer.

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
09:46

Problem 103

One means of air-conditioning hot summer air is by evaporative cooling, which is a process similar to the adiabatic saturation process. Consider outdoor ambient air at $35^{\circ} \mathrm{C}, 100 \mathrm{kPa}, 30 \%$ relative humidity. What is the maximum amount of cooling that can be achieved by such a technique? What disadvantage is there to this approach? Solve the problem using a first law analysis and repeat it using the psychrometric chart, Fig. E.4.

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
05:55

Problem 104

A flow of moist air at 45 $^{\circ} \mathrm{C}$, 10\% relative humidity with a fiow rate of $0.2 \mathrm{kg} / \mathrm{s}$ dry air is mixed with a flow of moist air at $25^{\circ} \mathrm{C}$, and absolute humidity of $\omega=0.018$ with a rate of $0.3 \mathrm{kg} / \mathrm{s}$ dry air. The mixing takes place in an air duct at $100 \mathrm{kPa},$ and there is no significant heat transfer. After the mixing, there is heat transfer to a final temperature of $40^{\circ} \mathrm{C}$. Find the temperature and relative humidity after mixing. Find the heat transfer and the final exit relative humidity.

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
05:24

Problem 105

An indoor pool evaporates $1.512 \mathrm{kg} / \mathrm{h}$ of water which is removed by a dehumidifier to maintain $21^{\circ} \mathrm{C}, \Phi=70 \%$ in the room. The dehumidifier, shown in Fig. $\mathrm{P} 12.105,$ is a refrigeration cycle in which air flowing over the evaporator cools such that liquid water drops out, and the air continues flowing over the condenser. For an airflow rate of $0.1 \mathrm{kg} / \mathrm{s}$ the unit requires $1.4 \mathrm{kW}$ input to a motor driving a fan and the compressor, and it has a coefficient of performance, $\beta=Q_{L} / W_{c}=$ 2.0. Find the state of the air as it returns to the room and the compressor work input.

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
02:48

Problem 106

Use the psychrometric chart to find the missing property of: $\Phi, \omega, T_{\mathrm{wel}}, T_{\mathrm{dry}}$
a. $T_{\mathrm{dry}}=25^{\circ} \mathrm{C}, \quad \Phi=80 \%$
b. $T_{\mathrm{dry}}=15^{\circ} \mathrm{C}, \quad \Phi=100 \%$
c. $T_{\text {dry }}=20^{\circ} \mathrm{C}, \quad \omega=0.008$
d. $T_{\mathrm{dry}}=25^{\circ} \mathrm{C}, \quad T_{\mathrm{wet}}=23^{\circ} \mathrm{C}$

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
02:37

Problem 107

Use the psychrometric chart to find the missing property of: $\Phi, \omega, T_{\mathrm{wat}}, T_{\mathrm{dry}}.$
a. $\quad \Phi=50 \%, \quad \omega=0.012$
b. $T_{\text {wet }}=15^{\circ} \mathrm{C}, \quad \Phi=60 \%$
c. $\quad \omega=0.008, \quad T_{\text {wet }}=17^{\circ} \mathrm{C}$
d. $T_{\text {dry }}=10^{\circ} \mathrm{C}, \quad \omega=0.006$

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
11:51

Problem 108

Use the formulas and the steam tables to find the missing property of: $\Phi, \omega,$ and $T_{\mathrm{dry}},$ total pres sure is $100 \mathrm{kPa}$. Repeat the answers using the psychrometric chart.
a. $\quad \Phi=50 \%, \quad \omega=0.010$
b. $T_{\text {wet }}=15^{\circ} \mathrm{C}, \quad \Phi=50 \%$
c. $T_{\mathrm{dry}}=25^{\circ} \mathrm{C}, \quad T_{\mathrm{xrt}}=21^{\circ} \mathrm{C}$

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
02:27

Problem 109

For each of the states in Problem 12.107 find the dew-point temperature.

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
02:13

Problem 110

Compare the weather in two places where it is cloudy and breezy. At beach $A$ the temperature
is $20^{\circ} \mathrm{C}$, the pressure is $103.5 \mathrm{kPa}$, and the relative humidity is $90 \% ;$ beach $B$ has $25^{\circ} \mathrm{C}, 99 \mathrm{kPa}$ and $20 \%$ relative humidity. Suppose you just took a swim and came out of the vater. Where would you feel more comfortable, and why?

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
01:14

Problem 111

Ambient air at $100 \mathrm{kPa}, 30^{\circ} \mathrm{C}$, and $40 \%$ relative humidity goes through a constant-pressure heat exchanger as a steady flow. In one case it is heated to $45^{\circ} \mathrm{C}$, and in another case it is cooled until it reaches saturation. For both cases find the exit relative humidity and the amount of heat transfer per kilogram of dry air.

Hast Aggarwal
Hast Aggarwal
Numerade Educator
04:42

Problem 112

A flow of moist air at $21^{\circ} \mathrm{C}$ with $60 \%$ relative humidity should be produced from mixing two different moist airflows. Flow 1 is at $10^{\circ} \mathrm{C}$ and $80 \%$ relative humidity; flow 2 is at $32^{\circ} \mathrm{C}$ and has $T_{\mathrm{wet}}=27^{\circ} \mathrm{C} .$ The mixing chamber can be followed by a heater or a cooler, as shown in Fig. P12.112. No liquid water is added, and $P=100$ kPa. Find the two controls- -one is the ratio of the two mass flow rates $\dot{m}_{a 1} / \dot{m}_{a 2}$ and the other is the heat transfer in the heater/cooler per kg dry air.

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
03:58

Problem 113

In a hot and dry climate, air enters an air-conditioner unit at $100 \mathrm{kPa}, 40^{\circ} \mathrm{C}$, and $5 \%$ relative humidity, at the steady rate of $1.0 \mathrm{m}^{3} / \mathrm{s}$. Liquid water at $20^{\circ} \mathrm{C}$ is sprayed into the air in the $\mathrm{AC}$ unit at the rate of $20 \mathrm{kg} / \mathrm{h},$ and heat is rejected from the unit at the rate $20 \mathrm{kW}$. The exit pressure is $100 \mathrm{kPa}$. What are the exit temperature and relative humidity?

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
02:27

Problem 114

Consider two states of atmospheric air. (1) $35^{\circ} \mathrm{C}$ $T_{\text {wet }}=18^{\circ} \mathrm{C}$ and $(2) 26.5^{\circ} \mathrm{C}, \Phi=60 \% .$ Suggest a system of devices that will allow air in a steady flow to change from (1) to (2) and from (2) to (1). Heaters, coolers, (de)humidifiers, liquid traps, and the like are available, and any liquid/solid flowing is assumed to be at the lowest temperature seen in the process. Find the specific and relative humidity for state $1,$ deiv point for state $2,$ and the heat transfer per kilogram dry air in each component in the systems.

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
02:31

Problem 115

To refresh air in a room, a counter flow heat exchanger, see Fig. P12.115, is mounted in the wall, drawing in outside air at $0.5^{\circ} \mathrm{C}, 80 \%$ relative humidity, and pushing out room air, $40^{\circ} \mathrm{C}$ $50 \%$ relative humidity. Assume an exchange of $3 \mathrm{kg} / \mathrm{min}$ dry air in a steady flow, and also assume that the room air exits the heat exchanger to the atmosphere at $23^{\circ} \mathrm{C}$. Find the net amount of water removed from the room, any liquid flow in the heat exchanger, and $(T, \Phi)$ for the fresh air entering the room.

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
08:34

Problem 116

Consider the mixing of a steam flow with an oxygen flow in Problem 12.71 . Find the rate of total inflowing availability and the rate of exergy destruction in the process.

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
02:50

Problem 117

A mixture of $75 \%$ carbon dioxide and $25 \%$ water by mass is flowing at $1600 \mathrm{K}, 100 \mathrm{kPa}$ into a heat exchanger where it is used to deliver energy to a heat engine. The mixture leaves the heat exchanger at $500 \mathrm{K}$ with a mass flow rate of $2 \mathrm{kg} / \mathrm{min} .$ Find the rate of energy and the rate of exergy delivered to the heat engine.

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
03:37

Problem 118

Find the second-law efficiency of the heat exchanger in Problem 12.59.

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
09:21

Problem 119

A piston/cylinder contains helium at $110 \mathrm{kPa}$ at ambient temperature $20^{\circ} \mathrm{C},$ and initial volume of $20 \mathrm{L}$ as shown in Fig. $\mathrm{P} 12.119 .$ The stops are mounted to give a maximum volume of $25 \mathrm{L}$ and the nitrogen line conditions are $300 \mathrm{kPa}$, $30^{\circ} \mathrm{C} .$ The valve is now opened, which allows nitrogen to flow in and mix with the helium. The valve is closed when the pressure inside reaches $200 \mathrm{kPa},$ at which point the temperature inside is $40^{\circ} \mathrm{C} .$ Is this process consistent with the second law of themodynamics?

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
07:02

Problem 120

A spherical balloon has an initial diameter of $1 \mathrm{m}$ and contains argon gas at $200 \mathrm{kPa}, 40^{\circ} \mathrm{C}.$ The balloon is connected by a valve to a $500-\mathrm{L}$ rigid tank containing carbon dioxide at $100 \mathrm{kPa}$ $100^{\circ} \mathrm{C} .$ The valve is opened, and eventually the balloon and tank reach a uniform state in which the pressure is $185 \mathrm{kPa}$. The balloon pressure is directly proportional to its diameter. Take the balloon and tank as a control volume, and calculate the final temperature and the heat transfer for the process.

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
09:48

Problem 121

An insulated vertical cylinder is fitted with a frictionless constant loaded piston of crosssectional area $0.1 \mathrm{m}^{2}$ and the initial cylinder height of $1.0 \mathrm{m}$. The cylinder contains methane gas at $300 \mathrm{K}, 150 \mathrm{kPa}$, and also inside is a $5-\mathrm{L}$ capsule containing neon gas at $300 \mathrm{K}, 500 \mathrm{kPa}$ shown in Fig. P12.121. The capsule now breaks, and the two gases mix together in a constantpressure process. What is the final temperature, final cylinder height, and net entropy change for the process?

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
07:56

Problem 122

An insulated rigid $2 \mathrm{m}^{3}$ tank $A$ contains $\mathrm{CO}_{2}$ gas at $200^{\circ} \mathrm{C}, 1 \mathrm{MPa} .$ An uninsulated rigid $1 \mathrm{m}^{3} \operatorname{tank} B$ contains ethane, $\mathrm{C}_{2} \mathrm{H}_{6},$ gas at $200 \mathrm{kPa}$, room temperature $20^{\circ} \mathrm{C}$. The two are connected by a oneway check valve that will allow gas from $A$ to $B$, but not from $B$ to $A$ shown in Fig. P12.122. The valve is opened and gas flows from $A$ to $B$ until the pressure in $B$ reaches 500 kPa when the valve is closed. The mixture in $B$ is kept at room temperature due to heat transfer. Find the total number of moles and the ethane mole fraction at the final state in $B$. Find the final temperature and pressure in tank $A$ and the heat transfer, to/from tank $B$.

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
09:59

Problem 123

A 0.2 $\mathrm{m}^{3}$ insulated, rigid vessel is divided into two equal parts $A$ and $B$ by an insulated partition, as shown in Fig. P.12.123. The partition will support a pressure difference of $400 \mathrm{kPa}$ before breaking. Side A contains methane and side B contains carbon dioxide. Both sides are initially at $1 \mathrm{MPa}, 30^{\circ} \mathrm{C}$. A valve on side $\mathrm{B}$ is opened, and carbon dioxide flows out. The carbon dioxide that remains in $\mathrm{B}$ is assumed to undergo a reversible adiabatic expansion while there is fiov out. Eventually the partition breaks, and the valve is closed. Calculate the net entropy change for the process that begins when the valve is closed.

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
10:59

Problem 124

An air-water vapor mixture enters a steady-flow heater humidifier unit at state $1: 10^{\circ} \mathrm{C}, 10 \%$ relative humidity, at the rate of $1 \mathrm{m}^{3} / \mathrm{s}$. A second air-vapor stream enters the unit at state $2: 20^{\circ} \mathrm{C}$ $20 \%$ relative humidity, at the rate of $2 \mathrm{m}^{3} / \mathrm{s} .$ Liquid water enters at state $3: 10^{\circ} \mathrm{C},$ at the rate of $400 \mathrm{kg}$ per hour. A single air-vapor flow exits the unit at state $4: 40^{\circ} \mathrm{C}$ shown in Fig. P12.124. Calculate the relative humidity of the exit flow and the rate of heat transfer to the unit.

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
03:45

Problem 125

You have just washed your hair and now blow dry it in a room with $23^{\circ} \mathrm{C}, \Phi=60 \%,(1) .$ The dryer, $500 \mathrm{W},$ heats the air to $49^{\circ} \mathrm{C},(2),$ blows it through your hair where the air becomes saturated $(3),$ and then flows on to hit a window where it cools to $15^{\circ} \mathrm{C}(4) .$ Find the relative humidity at state $2,$ the heat transfer per kilogram of dry air in the dryer, the airflow rate, and the amount of water condensed on the window, if any.

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
09:16

Problem 126

Steam power plants often utilize large cooling towers to cool the condenser cooling water so it can be recirculated; see Fig. P12.126. The process is essentially evaporative adiabatic cooling, in which part of the water is lost and must therefore be replenished. Consider the setup shown in Fig. $P 12.126,$ in which 1000 $\mathrm{kg} / \mathrm{s}$ of warm water at $32^{\circ} \mathrm{C}$ from the condenser enters the top of the cooling tower and the cooled water leaves the bottom at $20^{\circ} \mathrm{C}$. The moist ambient air enters the bottom at $100 \mathrm{kPa}$ dry-bulb temperature of $18^{\circ} \mathrm{C}$ and a wet-bulb temperature of $10^{\circ} \mathrm{C}$. The moist air leaves the tower at $95 \mathrm{kPa}, 30^{\circ} \mathrm{C}$, and relative humidity of $85 \% .$ Determine the required mass flow rate of dry air, and the fraction of the incoming water that evaporates and is lost.

Eric Mockensturm
Eric Mockensturm
Numerade Educator
06:56

Problem 127

Ambient air is at a condition of $100 \mathrm{kPa}, 35^{\circ} \mathrm{C}$ $50 \%$ relative humidity. A steady stream of air at $100 \mathrm{kPa}, 23^{\circ} \mathrm{C}, 70 \%$ relative humidity is to be produced by first cooling one stream to an appropriate temperature to condense out the proper amount of water and then mix this stream adiabatically with the second one at ambient conditions. What is the ratio of the two flow rates? To what temperature must the first stream be cooled?

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
05:10

Problem 128

A semipermeable membrane is used for the partial removal of oxygen from air that is blown through a grain elevator storage facility. Ambient air (79\% nitrogen, 21\% oxygen on a mole basis) is compressed to an appropriate pressure, cooled to ambient temperature $25^{\circ} \mathrm{C},$ and then fed through a bundle of hollow polymer fibers that selectively absorb oxygen, so the mixture leaving at $120 \mathrm{kPa}, 25^{\circ} \mathrm{C}$, contains only $5 \%$ oxygen, shown in Fig. $\mathrm{P} 12.128 .$ The absorbed oxy. gen is bled off through the fiber walls at $40 \mathrm{kPa}$, $25^{\circ} \mathrm{C},$ to a vacuum pump. Assume the process to be reversible and adiabatic and determine the minimum inlet air pressure to the fiber bundle.

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
04:41

Problem 129

A dehumidifier receives a flow of $0.25 \mathrm{kg} / \mathrm{s}$ moist air at $28^{\circ} \mathrm{C}, 80 \%$ relative humidity as shown in Figure $\mathrm{P} 12.105 .$ It is cooled down to $20^{\circ} \mathrm{C}$ as it flows over the evaporator and then heated up again as it flows over the condenser. The standard refrigeration cycle uses $R-22$ with an evaporator temperature of $5^{\circ} \mathrm{C}$ and a condensation pressure of $1600 \mathrm{kPa}$. Find the amount of liquid water removed and the heat transfer in the cooling process. How much compressor work is needed? What is the final air exit temperature and relative humidity?

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
12:08

Problem 130

$\mathrm{A} 100-\mathrm{L}$ insulated tank contains $\mathrm{N}_{2}$ gas at 200 $\mathrm{kPa}$ and ambient temperature $25^{\circ} \mathrm{C}$. The tank is connected by a valve to a supply line flowing $\mathrm{CO}_{2}$ at $1.2 \mathrm{MPa}, 90^{\circ} \mathrm{C} .$ A mixture of $50 \% \mathrm{N}_{2}$
$50 \% \mathrm{CO}_{2}$ by mole should be obtained by opening the valve and allowing $\mathrm{CO}_{2}$ to flow in until an appropriate pressure is reached, when the valve is closed. What is the pressure? The tank eventually cools to ambient temperature. Find the net entropy change for the overall process.

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
04:03

Problem 131

A cylinder/piston loaded with a linear spring contains saturated moist air at $120 \mathrm{kPa}, 0.1 \mathrm{m}^{3}$ volume and also $0.01 \mathrm{kg}$ of liquid water, all at ambient temperature $20^{\circ} \mathrm{C}$. The piston area is $0.2 \mathrm{m}^{2},$ and the spring constant is $20 \mathrm{kN} / \mathrm{m}$ This cylinder is attached by a valve to a line flowing dry air at $800 \mathrm{kPa}, 80^{\circ} \mathrm{C}$. The valve is opened, and air flows into the cylinder until the pressure reaches $200 \mathrm{kPa}$, at which point the temperature is $40^{\circ} \mathrm{C}$. Determine the relative humidity at the final state, the mass of air entering the cylinder, and the work done during the process.

Keshav Singh
Keshav Singh
Numerade Educator
View

Problem 132

Consider the previous problem and additionally determine the heat transfer. Show that the process does not violate the second law.

Nick Johnson
Nick Johnson
Numerade Educator
00:42

Problem 133

The air-conditioning by evaporative cooling in Problem 12.103 is modified by adding a dehumidification process before the water spray cooling process. This dehumidification is achieved as shown in Fig. $\mathrm{P} 12.133$ by using a desiccant material, which absorbs water on one side of a rotating drum heat exchanger. The desiccant is regenerated by heating on the other side of the drum to drive the water out. The pressure is 100 kPa everywhere, and other properties are on the diagram. Calculate the relative humidity of the cool air supplied to the room at state $4,$ and the heat transfer per unit mass of air that needs to be supplied to the heater unit.

Hast Aggarwal
Hast Aggarwal
Numerade Educator
02:06

Problem 134

If oxygen is $21 \%$ by mole of air, what is the oxygen state $(P, T, v)$ in a room at $540 \mathrm{R}, 15$ psia of total volume $2000 \mathrm{ft}^{3}$ ?

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
03:17

Problem 135

A flow of oxygen and one of nitrogen, both $540 \mathrm{R},$ are mixed to produce $1 \mathrm{lbm} / \mathrm{s}$ air at $540 \mathrm{R}, 15$ psia. What are the mass and volume flow rates of each line?

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
02:04

Problem 136

A flow of gas $A$ and a flow of gas $B$ are mixed in a 1: 1 mole ratio with same $T .$ What is the entropy generation per kmole flow out?

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
04:49

Problem 137

A rigid container has 1 lbm argon at 540 R and $1 \mathrm{lbm}$ argon at $720 \mathrm{R},$ both at 20 psia. Now they are allowed to mix without any external heat transfer. What is final $T$, $P$ ? Is any $s$ generated?

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
04:52

Problem 138

A rigid container has 1 $16 \mathrm{m} \mathrm{CO}_{2}$ at $540 \mathrm{R}$ and 1 lbm argon at $720 \mathrm{R}$, both at 20 psia. Now they are allowed to mix without any heat transfer. What is final $T, P ?$

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
02:17

Problem 139

A flow of 1 lom/s argon at 540 R and another flow of $1 \mathrm{lbm} / \mathrm{s} \mathrm{CO}_{2}$ at $2800 \mathrm{R}$, both at $20 \mathrm{psia}$ are mixed without any heat transfer. What is the exit $T, P ?$

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
05:37

Problem 140

What is the rate of entropy increase in Problem $12.139 ?$

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
03:07

Problem 141

If I have air at 14.7 psia and (a) $15 \mathrm{F}$, (b) 115 $\mathrm{F},$ and $(\mathrm{c}) 230 \mathrm{F},$ what is the maximum absolute humidity I can have?

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
04:16

Problem 142

A gas mixture at $250 \mathrm{F}, 18 \mathrm{lbf} / \mathrm{m} .^{2}$ is $50 \% \mathrm{N}_{2}$
$30 \% \mathrm{H}_{2} \mathrm{O},$ and $20 \% \mathrm{O}_{2}$ on a mole basis. Find the mass fractions, the mixture gas constant, and the volume for 10 lbm of mixture.

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
05:29

Problem 143

Weighing of masses gives a mixture at $80 \mathrm{F}$ 35 lbf/in $^{2}$ with 1 lbm $\mathrm{O}_{2}, 3 \mathrm{lbm} \mathrm{N}_{2},$ and $1 \mathrm{lbm}$ $\mathrm{CH}_{4} .$ Find the partial pressures of each component, the mixture specific volume (mass basis), the mixture molecular weight, and the total volume.

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
03:05

Problem 144

A new refrigerant $\mathrm{R}-410 \mathrm{a}$ is a mixture of $\mathrm{R}-32$ and $\mathrm{R}-125$ in a 1: 1 mass ratio. What is the overall molecular weight, the gas constant, and the ratio of specific heats for such a mixture?

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
01:49

Problem 145

A pipe flows $1.5 \mathrm{lbm} / \mathrm{s}$ of a mixture with mass fractions of $40 \% \mathrm{CO}_{2}$ and $60 \% \mathrm{N}_{2}$ at 60 lbf/in. $, 540$ R. Heating tape is wrapped around a section of pipe with insulation added, and 2 Btu/s electrical power is heating the pipe flow. Find the mixture exit temperature.

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
03:17

Problem 146

An insulated gas turbine receives a mixture of $10 \% \mathrm{CO}_{2}, 10 \% \mathrm{H}_{2} \mathrm{O},$ and $80 \% \mathrm{N}_{2}$ on a mass basis at $1800 \mathrm{R}, 75$ lbf/in. $^{2}$. The inlet volume flow rate is $70 \mathrm{ft}^{3} / \mathrm{s}$, and the exhaust is at 1300 $\mathrm{R}, 15$ lbf/in. $^{2}$. Find the power output in $\mathrm{Btu} / \mathrm{s}$ using constant specific heat from $\mathrm{F} 4$ at $540 \mathrm{R}$.

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
02:29

Problem 147

Solve Problem 12.146 using the values of enthalpy from Table F.6.

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
04:47

Problem 148

A piston cylinder device contains 0.3 $\mathrm{Hm}$ of a mixture of $40 \%$ methane and $60 \%$ propane by mass at $540 \mathrm{R}$ and 15 psia. The gas is now slowly compressed in an isothermal $(T=\mathrm{con}-$ stant) process to a final pressure of 40 psia. Show the process in a $P-V$ diagram, and find both the work and heat transfer in the process.

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
06:32

Problem 149

A mixture of 4 lbm oxygen and 4 lbm of argon is in an insulated piston cylinder arrangement at $14.7 \mathrm{lbf} / \mathrm{in.}^{2}, 540 \mathrm{R} .$ The piston now compresses the mixture to half its initial volume. Find the final pressure, temperature, and the piston work.

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
05:56

Problem 150

Two insulated tanks $A$ and $B$ are connected by a valve. Tank $A$ has a volume of $30 \mathrm{ft}^{3}$ and initially contains argon at $50 \mathrm{lbf} / \mathrm{in.}^{2}, 50 \mathrm{F}$. Tank $B$ has a volume of $60 \mathrm{ft}^{3}$ and initially contains ethane at 30 lbffin. 120 F. The valve is opened and remains open until the resulting gas mixture comes to a uniform state. Find the final pressure and temperature.

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
05:25

Problem 151

A mixture of $50 \%$ carbon dioxide and $50 \%$ water by mass is brought from $2800 \mathrm{R}, 150$ $\mathrm{Hf} / \mathrm{in} .^{2}$ to $900 \mathrm{R}, 30 \mathrm{lbf} / \mathrm{in}^{2}$ in a polytropic
process through a steady-flow device. Find the necessary heat transfer and work involved using values from F.4.

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
08:45

Problem 152

Carbon dioxide gas at $580 \mathrm{R}$ is mixed with nitrogen at $500 \mathrm{R}$ in an insulated mixing chamber. Both flows are at $14.7 \mathrm{lbf} / \mathrm{in.}^{2}$, and the mole ratio of carbon dioxide to nitrogen is 2: 1 Find the exit temperature and the total entropy generation per mole of the exit mixture.

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
06:16

Problem 153

A mixture of 60\% helium and 40\% nitrogen by mole enters a turbine at $150 \mathrm{lbf} / \mathrm{in.}^{2}, 1500 \mathrm{R}$ at a rate of $4 \mathrm{lbm} / \mathrm{s}$. The adiabatic turbine has an exit pressure of $15 ~ 16 \mathrm{ff} / \mathrm{in} .^{2}$ and an insentropic efficiency of $85 \%$. Find the turbine work.

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
06:52

Problem 154

A large air separation plant, see Fig. P12.68, takes in ambient air $(79 \%) \mathrm{N}_{2}, 21 \% \mathrm{O}_{2}$ by volume) at $14,7 \mathrm{lbf} / \mathrm{jn}_{1}^{2}, 70 \mathrm{F}$ at a rate of $2 \mathrm{lb}$ $\mathrm{mol} / \mathrm{s} .$ It discharges a stream of pure $\mathrm{O}_{2}$ gas at $30 \mathrm{lbf} / \mathrm{in.}^{2}, 200 \mathrm{F},$ and a stream of pure $\mathrm{N}_{2}$ gas
at $14.7 \mathrm{lbf} / \mathrm{in.}^{2}, 70 \mathrm{F}$. The plant operates on an electrical power input of $2000 \mathrm{kW}$. Calculate the net rate of entropy change for the process.

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
08:38

Problem 155

A tank has two sides initially separated by a diaphragm. Side A contains 2 $\mathrm{Hm}$ of water, and side $B$ contains $2.4 \mathrm{lbm}$ of air-both at $68 \mathrm{F}$ $14.7 \mathrm{lb} \mathrm{f} / \mathrm{in.}^{2} .$ The diaphragm is now broken, and the whole tank is heated to $1100 \mathrm{F}$ by a $1300 \mathrm{F}$ reservoir. Find the final total pressure, heat transfer, and total entropy generation.

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
10:20

Problem 156

Find the entropy generation for the process in Problem $12.150 \mathrm{E}.$

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
02:56

Problem 157

Consider a volume of $2000 \mathrm{ft}^{3}$ that contains an air-water vapor mixture at $14.7 \mathrm{lbf} / \mathrm{in.}^{2}, 60 \mathrm{F}$ and $40 \%$ relative humidity. Find the mass of water and the humidity ratio. What is the dew point of the mixture?

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
04:27

Problem 158

A $1 \mathrm{lbm} / \mathrm{s}$ flow of saturated moist air (relative humidity $100 \%$ ) at 14.7 psia and 50 F goes through a heat exchanger and comes out at 80 F. What is the exit relative humidity, and how much power is needed?

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
04:42

Problem 159

Consider a $10-\mathrm{ft}^{3}$ rigid tank containing an air-water vapor mixture at $14.7 \mathrm{lbf} / \mathrm{in.}^{2}, 90 \mathrm{F}$ with $70 \%$ relative humidity. The system is cooled until the water just begins to condense. Determine the final temperature in the tank and the heat transfer for the process.

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
04:16

Problem 160

Consider at $35 \mathrm{ft}^{3} / \mathrm{s}$ flow of atmospheric air at $14.7 \mathrm{psia}, 80 \mathrm{F},$ and $80 \%$ relative humidity. Assume this flows into a basement room where it cools to $60 \mathrm{F}$ at 14.7 psia. How much liquid will condense out?

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
06:05

Problem 161

Air in a piston/cylinder is at $95 \mathrm{F}, 15 \mathrm{lbf} / \mathrm{in}$. $^{2}$ and relative humidity of $80 \%$. It is now compressed to a pressure of 75 lbf/in. $^{2}$ in a constanttemperature process. Find the final relative and specific humidity and the volume ratio $V_{2} / V_{1}.$

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
05:24

Problem 162

A $10-\mathrm{ft}^{3}$ rigid vessel initially contains moist air at $20 \mathrm{lb}$ f/in. $^{2}, 100 \mathrm{F}$, with a relative humidity of $10 \% .$ A supply line connected to this vessel by a valve carries steam at 100 lbf/in.', 400 F. The valve is opened, and steam flows into the vessel until the relative humidity of the resultant moist air mixture is $90 \% .$ Then the valve is closed. Sufficient heat is transferred from the vessel so the temperature remains at $100 \mathrm{F}$ during the process. Determine the heat transfer for the process, the mass of steam entering the vessel, and the final pressure inside the vessel.

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
12:40

Problem 163

A water-filled reactor of $50 \mathrm{ft}^{3}$ is at 2000 $16 \mathrm{f} / \mathrm{in} .^{2}, 550 \mathrm{F}$, and located inside an insulated containment room of $5000 \mathrm{ft}^{3}$ that has air at $1 \mathrm{atm} .$ and $77 \mathrm{F}$. Due to a failure, the reactor ruptures and the water fills the containment room. Find the final quality and pressure by iterations.

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
06:23

Problem 164

Two moist air streams with $85 \%$ relative humidity, both flowing at a rate of $0.2 \mathrm{lbm} / \mathrm{s}$ of dry air are mixed in a steady flow setup. One inlet fiowstream is at $90 \mathrm{F}$, and the other at 61 F. Find the exit relative humidity.

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
06:11

Problem 165

A flow of moist air from a domestic fumace, state 1 in Fig. $\mathrm{P} 12.98$ is at $120 \mathrm{F}, 10 \%$ relative humidity with a flow rate of $0.1 \mathrm{lbm} / \mathrm{s}$ dry air. 14.7 psia, generated from tap water at 60 F. $U_{\mathrm{P}}$ in the living room the flow comes out at state 4: 90 $\mathrm{F}, 60 \%$ relative humidity. Find the power needed for the electric heater and the heat transfer to the flow from state 1 to state 4.

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
06:01

Problem 166

Atmospheric air at $95 \mathrm{F}$, relative humidity of $10 \%,$ is too warm and also too dry. An air conditioner should deliver air at $70 \mathrm{F}$, and $50 \%$ relative humidity in the amount of $3600 \mathrm{ft}^{3}$ per hour. Sketch a setup to accomplish this; find any amount of liquid (at $68 \mathrm{F}$ ) that is needed or discarded and any heat transfer.

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
11:42

Problem 167

An indoor pool evaporates $3 \mathrm{lbm} / \mathrm{h}$ of water which is removed by a dehumidifier to maintain $70 \mathrm{F}, \Phi=70 \%$ in the room. The dehumidifier is a refrigeration cycle in which air flowing over the evaporator cools such that liquid water drops out, and the air continues flowing over the condenser, as shown in Fig. P12.105. For an airflow rate of $0.2 \mathrm{lbm} / \mathrm{s}$, the unit requires 1.2 $\mathrm{B}$ tu/s input to a motor driving a fan and the compressor, and it has a coefficient of performance, $\beta=\dot{Q}_{L} / \dot{W}_{c}=2.0 .$ Find the state of the air after the evaporator, $T_{2}, \omega_{2}, \Phi_{2},$ and the heat, rejected. Find the state of the air as it returns to the room and the compressor work input.

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
09:59

Problem 168

To refresh air in a room, a counterflow heat exchanger is mounted in the wall, as shown in Fig. P12.115. It draws in outside air at $33 \mathrm{F}$, $80 \%$ relative humidity, and draws room air, $104 \mathrm{F}, 50 \%$ relative humidity, out. Assume an exchange of 6 lbm/min dry air in a steady-flow device, and also that the room air exits the heat exchanger to the atmosphere at 72 F. Find the net amount of water removed from the room, any liquid flow in the heat exchanger, and $(T, \Phi)$ for the fresh air entering the room.

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
02:06

Problem 169

Ambient air is at a condition of $14.7 \mathrm{lbf} / \mathrm{in.}^{2}$ $95 \mathrm{F}, 50 \%$ relative humidity. A steady stream of air at $14.7 \mathrm{lbf} / \mathrm{in.}^{2}, 73 \mathrm{F}, 70 \%$ relative humidity is to be produced by first cooling one stream to an appropriate temperature to condense out the proper amount of water and then mix this stream adiabatically with the second one at ambient conditions. What is the ratio of the two flow rates? To what temperature must the first stream be cooled?

Hast Aggarwal
Hast Aggarwal
Numerade Educator
10:01

Problem 170

A 4-ft insulated tank contains nitrogen gas at 30 Ibf/in. $^{2}$ and ambient temperature 77 F. The tank is connected by a valve to a supply line flowing carbon dioxide at $180 \mathrm{lbf} / \mathrm{in.}^{2}, 190 \mathrm{F}$. A mixture of 50 mole percent nitrogen and 50 mole percent carbon dioxide is to be obtained by opening the valve and allowing flow into the tank until an appropriate pressure is reached, when the valve is closed. What is the pressure? The tank eventually cools to ambient temperature. Calculate the net entropy change for the overall process.

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
09:02

Problem 171

Write a program to solve the general case of Problems $12.53 / 74$ in which the two volumes and the initial state properties of the argon and the ethane are input variables. Use constant specific heat from Table A.5.

Mohammad Mehran
Mohammad Mehran
Numerade Educator
01:32

Problem 172

Mixing of $\mathrm{CO}_{2}$ and $\mathrm{N}_{2}$ in a steady-flow setup was given in Problem $12.62 .$ If the temperatures are very different an assumption of constant specific heat is inappropriate. Study the problem assuming the $\mathrm{CO}_{2}$ enters at $300 \mathrm{K}, 100 \mathrm{kPa},$ as a function of the $N_{2}$ inlet temperature using specific heat from Table $A .7$ or the formula in A.6. Give the nitrogen inlet temperature for which the constant specific heat assumption starts to be more than $1 \%, 5 \%,$ and $10 \%$ wrong for the exit mixture temperature.

Hast Aggarwal
Hast Aggarwal
Numerade Educator
01:19

Problem 173

The setup in Problem 12.97 is similar to a process that can be used to produce dry powder from a slurry of water and dry material as coffee or milk. The water flow at state 3 is a mixture of $80 \%$ liquid water and $20 \%$ dry material on a mass basis with $C_{\mathrm{dy}}=0.4 \mathrm{kJ} / \mathrm{kg}$ K. After the water is evaporated, the dry material falls to the bottom and is removed in an additional line, $\dot{m}_{\mathrm{dry}}$ exit at state $4 .$ Assume a reasonable $T_{4}$ and that state 1 is heated atmospheric air. Investigate the inlet flow temperature as a function of state humidity ratio.

Penny Riley
Penny Riley
Numerade Educator
04:22

Problem 174

A dehumidifier for household applications is similar to the system shown in Fig. P12.105. Study the requirements to the refrigeration cycle as a function of the atmospheric conditions and include a worst case estimation.

Anjana Saravanan
Anjana Saravanan
Numerade Educator
02:02

Problem 175

A clothes dryer has a $60^{\circ} \mathrm{C}, \Phi=90 \%$ airflow out at a rate of $3 \mathrm{kg} / \mathrm{min}$. The atmospheric conditions are $20^{\circ} \mathrm{C}$, relative humidity of $50 \%$. How much water is carried away and how much power is needed? To increase the efficiency, a counterflow heat exchanger is installed to preheat the incoming atmospheric air up with the hot exit flow. Estimate suitable exit temperatures from the heat exchanger and investigate the design changes to the clothes dryer. (What happens to the condensed water?) How much energy can be saved this way?

Kratika Bhadauria
Kratika Bhadauria
Numerade Educator
13:58

Problem 176

Addition of steam to combustors in gas turbines and to internal-combustion engines reduces the peak temperatures and lowers emission of $\mathrm{NO}$ Consider a modification to a gas turbine, as shown in Fig. $\mathrm{P} 12.176,$ where the modified cycle is called the Cheng cycle. In this example, it is used for a cogenerating power plant. Assume $12 \mathrm{kg} / \mathrm{s}$ air with state 2 at $1.25 \mathrm{MPa}$, unknown temperature, is mixed with $2.5 \mathrm{kg} / \mathrm{s}$ water at $450^{\circ} \mathrm{C}$ at constant pressure before the inlet to the turbine. The turbine exit temperature is $T_{4}=$ $500^{\circ} \mathrm{C},$ and the pressure is 125 kPa. For a reasonable turbine efficiency, estimate the required air temperature at state 2. Compare the result to the case where no steam is added to the mixing chamber and only air runs through the turbine.

Eric Mockensturm
Eric Mockensturm
Numerade Educator
02:47

Problem 177

Consider the district water heater acting as the condenser for part of the water between states 5 and 6 in Fig. $P 12.176 .$ If the temperature of the mixture $(12 \mathrm{kg} / \mathrm{s} \text { air, } 2.5 \mathrm{kg} / \mathrm{s} \text { steam })$ at state 5 is $135^{\circ} \mathrm{C},$ make a study of the district heating load, $Q_{1},$ as a function of the exit temperature $T_{6}$ Study also the sensitivity of the results with respect to the assumption that state 6 is saturated moist air.

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
02:27

Problem 178

The cogeneration gas-turbine cycle can be augmented with a heat pump to extract more energy from the turbine exhaust gas, as shown in Fig. P12.178. The heat pump upgrades the energy to be delivered at the $70^{\circ} \mathrm{C}$ line for district heating. In the modified application, the first heat exchanger has exit temperature $T_{6 a}=T_{7 a}=45^{\circ} \mathrm{C}$ and the second one has $T_{6 b}=T_{7 b}=36^{\circ} \mathrm{C} .$ Assume the district heating line has the same exit temperature as before so this arrangement allows for a higher flow rate. Estimate the increase in the district heating load that can be obtained and the necessary work input to the heat pump.

Banhishikha Sinha
Banhishikha Sinha
Numerade Educator
04:41

Problem 179

Several applications of dehumidification do not rely on water condensation by cooling. A desiccant with a greater affinity to water can absorb water directly from the air accompanied by a heat release. The desiccant is then regenerated by heating, driving the water out. Make a list of several such materials as liquids, gels, and solids and show examples of their use.

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator