Fundamentals of Thermodynamics

Claus Borgnakke, Richard E. Sonntag

Chapter 3 First Law of Thermodynamics and Energy Equation - all with Video Answers

Educators

Chapter Questions

00:55

Problem 1

What is 1 cal in SI units and what is the name given to $1 \mathrm{~N}-\mathrm{m} ?$

Ali Beker

Numerade Educator

01:02

Problem 2

A car engine is rated at $110 \mathrm{~kW}$. What is the power in hp?

Ali Beker

Numerade Educator

02:53

Problem 3

Why do we write $\Delta E$ or $E_{2}-E_{1},$ whereas we write ${ }_{1} Q_{2}$ and ${ }_{1} W_{2} ?$

Jacob Adamczyk

Numerade Educator

01:40

Problem 4

If a process in a control mass increases energy $E_{2}-$ $E_{1}>0,$ can you say anything about the sign for ${ }_{1} Q_{2}$ and $_{1} W_{2} ?$

Mohammad Mehran

Numerade Educator

03:38

In Fig. $\mathrm{P} 3.5, \mathrm{CV} A$ is the mass inside a piston/ cylinder, and $\mathrm{CV} B$ is the mass plus the piston outside, which is the standard atmosphere. Write the energy equation and work term for the two CVs, assuming we have a nonzero $Q$ between state 1 and state 2.

Mohammad Mehran

Numerade Educator

04:08

Problem 6

A 500 -W electric space heater with a small fan inside heats air by blowing it over a hot electrical wire. For each control volume $-$ (a) wire only, (b) all the room air, and (c) total room air plus the heater-specify the storage, work, and heat transfer terms as $+500 \mathrm{~W}$ or $-500 \mathrm{~W}$ or 0 (neglect any $\dot{Q}$ through the room walls or windows).

Mohammad Mehran

Numerade Educator

04:04

Problem 7

Two engines provide the same amount of work to lift a hoist. One engine provides a force of $3 \mathrm{~F}$ in a cable and the other provided 1 F. What can you say about the motion of the point where the force acts in the two engines?

Mohammad Mehran

Numerade Educator

01:13

Problem 8

Two hydraulic piston/cylinders are connected through a hydraulic line, so they have roughly the same pressure. If they have diameters of $D_{1}$ and $D_{2}=2 D_{1},$ respectively, what can you say about the piston forces $F_{1}$ and $F_{2} ?$

You heat a gas $10 \mathrm{~K}$ at $P=C .$ Which one in Table $\mathrm{A} .5$ requires most energy? Why?

Indicate the location of the four states in Problem 3.71 as points in both the $P-v$ and $T-v$ diagrams.

Mohammad Mehran

Numerade Educator

07:36

Problem 73

A 100 -L rigid tank contains nitrogen $\left(\mathrm{N}_{2}\right)$ at $900 \mathrm{~K}$ and $3 \mathrm{MPa}$. The tank is now cooled to $100 \mathrm{~K}$. What are the work and heat transfer for the process?

Consider the piston/cylinder arrangement shown in Fig. P3.234. A frictionless piston is free to move between two sets of stops. When the piston rests on the lower stops, the enclosed volume is $400 \mathrm{~L}$. When the piston reaches the upper stops, the volume is $600 \mathrm{~L}$. The cylinder initially contains water at $100 \mathrm{kPa}$, with $20 \%$ quality. It is heated until the water eventually exists as saturated vapor. The mass of the piston requires $300 \mathrm{kPa}$ pressure to move it against the outside ambient pressure. Determine the final pressure in the cylinder, the heat transfer, and the work for the overall process.

An insulated cylinder is divided into two parts of $10 \mathrm{ft}^{3}$ each by an initially locked piston. Side $A$ has air at $2 \mathrm{~atm}, 600 \mathrm{R},$ and side $B$ has air at $10 \mathrm{~atm}, 2000 \mathrm{R},$ as shown in Fig. $\mathrm{P} 3.151 .$ The piston is now unlocked so that it is free to move, and it conducts heat so that the air comes to a uniform temperature $T_{A}=T_{B} .$ Find the mass in both $A$ and $B$, and also the final $T$ and $P$.

Keshav Singh

Numerade Educator

07:16

Problem 307

A piston/cylinder arrangement of initial volume $0.025 \mathrm{~m}^{3}$ contains saturated water vapor at $200^{\circ} \mathrm{C} .$ The steam now expands in a quasi-equilibrium isothermal process to a final pressure of $200 \mathrm{kPa}$ while it does work against the piston. Determine the work done in this process by a numerical integration (summation) of the area below the $P-V$ process curve. Compute about 10 points along the curve by using the computerized software to find the volume at $200^{\circ} \mathrm{C}$ and the various pressures. How different is the work calculated if ideal gas is assumed?

Keshav Singh

Numerade Educator

04:26

Problem 308

Reconsider the process in Problem $3.170,$ in which three states were specified. Solve the problem by fitting a single smooth curve $(P$ versus $v)$ through the three points. Map out the path followed (including temperature and quality) during the process.

Mohammad Mehran

Numerade Educator

04:07

Problem 309

Ammonia vapor is compressed inside a cylinder by an external force acting on the piston. The ammonia is initially at $30^{\circ} \mathrm{C}, 500 \mathrm{kPa},$ and the final pressure is $1400 \mathrm{kPa}$. The following data have been measured for the process:
$$
\begin{array}{|cccccccc|}
\hline \begin{array}{c}
\text { Pressure, } \\
\mathrm{kPa}
\end{array} & 500 & 653 & 802 & 945 & 1100 & 1248 & 1400 \\
\text { Volume, } \mathrm{L} & 1.25 & 1.08 & 0.96 & 0.84 & 0.72 & 0.60 & 0.50 \\
\hline
\end{array}
$$
Determine the work done by the ammonia by summing the area below the $P-V$ process curve. As you plot it, $P$ is the height and the change in volume is the base of a number of rectangles.

Saikat Chatterjee

Numerade Educator

07:44

Problem 310

Use the supplied software to track the process in Problem 3.96 in steps of $10^{\circ} \mathrm{C}$ until the two-phase region is reached, after that step with jumps of $5 \%$ in the quality. At each step write out $T, x,$ and the heat transfer to reach that state from the initial
state.

Uma Kumari

Numerade Educator

06:45

Problem 311

Examine the sensitivity of the final pressure to the containment room volume in Problem 3.101 . Solve for the volume for a range of final pressures, $100-250 \mathrm{kPa},$ and sketch the pressure versus volume curve.

Mohammad Mehran

Numerade Educator

03:09

Problem 312

Using states with given $(P, v)$ and properties from the supplied software, track the process in Problem 3.105. Select five pressures away from the initial toward the final pressure so that you can plot the temperature, the heat added, and the work given out as a function of the volume.

Vipender Yadav

Numerade Educator

01:23

Problem 313

Track the process described in Problem 3.115 so that you can sketch the amount of heat transfer added and the work given out as a function of the volume.

Hast Aggarwal

Numerade Educator

13:21

Problem 314

Write a program to solve Problem 3.123 for a range of initial velocities. Let the car mass and final velocity be input variables.

Eric Mockensturm

Numerade Educator

06:56

Problem 315

For one of the substances in Table A.6, compare the enthalpy change between any two temperatures, $T_{1}$ and $T_{2},$ as calculated by integrating the specific heat equation; by assuming constant specific heat at the average temperature; and by assuming constant specific heat at temperature $T_{1}$.

Mohammad Mehran

Numerade Educator

24:07

Problem 316

Consider a general version of Problem 3.144 with a substance listed in Table A.6. Write a program where the initial temperature and pressure and the final temperature are program inputs.

Eric Mockensturm

Numerade Educator

04:23

Problem 317

Write a program for Problem $3.163,$ where the initial state, the volume ratio, and the polytropic exponent are input variables. To simplify the formulation, use constant specific heat.

Eric Mockensturm

Numerade Educator

05:19

Problem 318

Examine a process whereby air at $300 \mathrm{~K}, 100 \mathrm{kPa}$ is compressed in a piston/cylinder arrangement to $600 \mathrm{kPa} .$ Assume the process is polytropic with exponents in the $1.2-1.6$ range. Find the work and heat transfer per unit mass of air. Discuss the different cases and how they may be accomplished by insulating the cylinder or by providing heating or cooling.

Keshav Singh

Numerade Educator

05:31

Problem 319

A cylindrical tank of height $2 \mathrm{~m}$ with a crosssectional area of $0.5 \mathrm{~m}^{2}$ contains hot water at $80^{\circ} \mathrm{C}$. $125 \mathrm{kPa}$. It is in a room with temperature $T_{0}=$ $20^{\circ} \mathrm{C}$, so it slowly loses energy to the room air proportional to the temperature difference as
$$
\dot{Q}_{\text {loss }}=C A\left(T-T_{0}\right)
$$
with the tank surface area, $A,$ and $C$ is a constant. For different values of the constant $C,$ estimate the time it takes to bring the water to $50^{\circ} \mathrm{C}$. Make enough simplifying assumptions so that you can solve the problem mathematically, that is find a formula for $T(t)$

Mohammad Mehran

Numerade Educator