Essential College Physics

Andrew F. Rex, Richard Wolfson

Chapter 14

The Laws of Thermodynamics - all with Video Answers

Educators

Chapter Questions

Problem 1

Compare the work done in compressing a gas (a) at constant pressure, (b) adiabatically, and (c) isothermally.

Ajay Singhal

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Problem 2

After you use a hand pump to inflate a bicycle tire, why is the pump hot? Why does the tire also feel warm?

Ajay Singhal

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Problem 3

Does the temperature of a gas necessarily increase if simultaneously (a) heat flows in while the gas is compressed and (b) heat flows in while the gas expands?

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Problem 4

What happens to a gas's temperature when it (a) expands adiabatically and (b) is compressed adiabatically?

Shahab Ullah

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Problem 5

Exercising vigorously, you do work on your surroundings, so $W<0 .$ You also transfer heat to your surroundings, so $Q<0$ With $W<0$ and $Q<0$, why doesn't your body temperature drop?

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Problem 6

A heat pump uses electrical energy at a rate of $500 \mathrm{~W}$. How can it deliver more than $500 \mathrm{~W}$ of heat without violating some law of thermodynamics?

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Problem 7

Why are air conditioners put in windows instead of in the middle of rooms?

Shahab Ullah

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Problem 8

In a Carnot engine, the temperature of the hot reservoir is increased. Does this increase or decrease the engine's efficiency?

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Problem 9

Why can't you cool the room by leaving your refrigerator door open?

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Problem 10

Assume your house is warmer in summer than in winter. Does it take more or less energy to run your refrigerator in summer?

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Problem 11

Which has more entropy, a piece of silver when it's solid or when it's liquid?

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Problem 12

If you mix hot water and cold water, the mixture comes to equilibrium at some intermediate temperature. Has the entropy of the system increased?

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Problem 13

Suppose the two-chambered box in Section 14.5 contains 50 molecules in each side. As the molecules move randomly, a short time later there are 48 on one side and 52 on the other. Does this constitute a violation of the second law?

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Problem 14

In an example of free expansion, a gas doubles its volume by expanding into a vacuum without pushing on anything. Discuss whether each of the following quantities increase, decrease, or remain the same: pressure, temperature, and entropy.

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Problem 15

Give an example not mentioned in this chapter in which the first law of thermodynamics is satisfied but the second law would be violated.

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Problem 16

Heat flows into a system during (a) adiabatic expansion; (b) adiabatic compression; (c) isothermal compression; (d) isothermal expansion.

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Problem 17

A monatomic ideal gas occupies $23.0 \mathrm{~L}$ at 1 atm pressure. Its internal energy is (a) $2300 \mathrm{~J} ;$ (b) $2800 \mathrm{~J} ;$ (c) $3100 \mathrm{~J} ;$ (d) $3500 \mathrm{~J}$.

Narayan Hari

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Problem 18

A cylinder with a movable piston encloses 0.25 mole of ideal gas at $300 \mathrm{~K}$. How much heat is required to increase its volume isothermally by a factor of 2 ? (a) $430 \mathrm{~J} ;$ (b) $620 \mathrm{~J}$;
(c) $900 \mathrm{~J}$;
(d) $1730 \mathrm{~J}$.

Narayan Hari

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Problem 19

In an adiabatic compression, a gas's temperature (a) increases;
(b) decreases; (c) remains the same; (d) cannot be determined from the information given.

Shahab Ullah

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Problem 20

2.5 moles of neon gas expand adiabatically and in the process do $930 \mathrm{~J}$ of work. The gas's temperature drops by
(a) $10^{\circ} \mathrm{C}$
(b) $30^{\circ} \mathrm{C} ;$ (c) $45^{\circ} \mathrm{C}$
(d) $60^{\circ} \mathrm{C}$.

Narayan Hari

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Problem 21

Consider a closed cycle on a pressure-versus-volume graph that is, a cycle in which a gas returns to its initial state, as shown in Figure $\mathrm{MCl}$ 4. $21 .$ The work done on the gas is positive
(a) if the path is traversed clockwise; (b) if the path is traversed $\quad$ counterclockwise;
(c) always; (d) never.

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Problem 22

What's the entropy change of a $50-\mathrm{g}$ ice cube that melts at $0^{\circ} \mathrm{C} ?$
(a) $-14 \mathrm{~J} / \mathrm{K}$;
(b) $42 \mathrm{~J} / \mathrm{K} ;$ (c) $61 \mathrm{~J} / \mathrm{K}$;
(d) $85 \mathrm{~J} / \mathrm{K}$.

Shahab Ullah

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Problem 23

What's the entropy change of $40 \mathrm{~g}$ of water that freezes at $0^{\circ} \mathrm{C} ?$
(a) $-39 \mathrm{~J} / \mathrm{K} ;$ (b) $-49 \mathrm{~J} / \mathrm{K} ;$ (c) $-59 \mathrm{~J} / \mathrm{K} ;$ (d) $-69 \mathrm{~J} / \mathrm{K}$.

Shahab Ullah

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Problem 24

A heat engine does $800 \mathrm{~J}$ of work and dumps $1400 \mathrm{~J}$ of heat to the cold reservoir. What's its efficiency?
(a) 0.22 ;
(b) 0.36;
(d) 0.64 .
(c) 0.57

Shahab Ullah

Numerade Educator

Problem 25

A refrigerator with $\mathrm{COP}=3.5$ draws $800 \mathrm{~W}$ of electric power. At what rate can this refrigerator remove heat from its interior?
(a) $229 \mathrm{~W}$;
(b) $2000 \mathrm{~W}$;
(c) $2800 \mathrm{~W}$ :
(d) $3600 \mathrm{~W}$.

Shahab Ullah

Numerade Educator

Problem 26

What's the maximum efficiency for a heat engine operating
between $273 \mathrm{~K}$ and $400 \mathrm{~K} ?$ (a) $0.32 ;$ (b) $0.44 ;$ (c) $0.56 ;$ d) 0.68 .

Shahab Ullah

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Problem 27

Find the internal-energy change when 1.25 mol of helium gas is warmed by $100^{\circ} \mathrm{C}$

Narayan Hari

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Problem 28

Find the internal-energy change when 1.25 mol of oxygen $\left(\mathrm{O}_{2}\right)$ gas is warmed by $100^{\circ} \mathrm{C}$.

Narayan Hari

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Problem 29

Find the rate of heat flow into a system whose internal energy is increasing at the rate of $45 \mathrm{~W}$, given that the system is doing work at a rate of $165 \mathrm{~W}$.

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Problem 30

In a perfectly insulated container, $1.0 \mathrm{~kg}$ of water is stirred vigorously until its temperature rises by $7.0^{\circ} \mathrm{C}$. How much work was done on the water?

Nathan Silvano

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Problem 31

Krypton is a monatomic ideal gas. Suppose you have 4.0 moles of krypton at $293 \mathrm{~K}$ and 1 atm. After absorbing $1830 \mathrm{~J}$ of heat, the gas temperature has increased by $45^{\circ} \mathrm{C}$. (a) How much work is involved in this process? (b) Does the gas volume increase or decrease? (c) Repeat parts (a) and (b) if the same heat flow results in a temperature increase of only $15^{\circ} \mathrm{C}$.

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Problem 32

Show that $\mathrm{U}=\frac{3}{2} P V$ for a monatomic ideal gas.

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Problem 33

Find the internal energy of $2.0 \mathrm{~mol}$ of argon at $273 \mathrm{~K}$ and 1.0 atm. If the gas pressure and volume both double, what's the change in internal energy?

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Problem 34

The combustion of $1 \mathrm{~L}$ of gasoline releases about $3.4 \times 10^{7} \mathrm{~J}$ of energy. In one car's engine, about $80 \%$ of that energy is lost as heat. (a) How much work is done by the engine for each liter of gasoline burned? (b) If the car requires $4.5 \times 10^{5} \mathrm{~J}$ of work to travel $1 \mathrm{~km},$ find the fuel efficiency in $\mathrm{km} / \mathrm{L}$.

Narayan Hari

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Problem 35

An 8.5 - $L$ nitrogen-filled balloon is heated in a warm oven and absorbs $860 \mathrm{~J}$ of heat. If its temperature increases by $82^{\circ} \mathrm{C}$, how much work is done on the gas?

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Problem 36

A balloon contains $2.5 \mathrm{~L}$ of oxygen gas at $1.0 \mathrm{~atm}$ and $20{ }^{\circ} \mathrm{C}$. How much work is done in compressing the balloon at constant pressure until its volume drops by $10 \% ?$

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Problem 37

For the situation of the preceding problem, find (a) the increase in the gas temperature and (b) the heat that must then be removed to return the gas to its original temperature.

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Problem 38

A balloon contains 0.30 mol of helium. It rises, maintaining a constant $300-\mathrm{K}$ temperature, to an altitude where its volume has expanded five times. How much work is done by the gas during this isothermal expansion? Neglect tension forces in the balloon.

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Problem 39

The balloon in the preceding problem starts at a pressure of $100 \mathrm{kPa}$ and rises to an altitude where the pressure is $75 \mathrm{kPa}$ maintaining a constant $300 \mathrm{~K}$ temperature. (a) By what factor does its volume increase? (b) How much work does the gas do?

Ajay Singhal

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Problem 40

A balloon contains $2.0 \mathrm{~mol}$ of helium at $1.0 \mathrm{~atm}$, initially at $200^{\circ} \mathrm{C}$. (a) What's the initial volume? (b) What's the volume after the gas cools at constant pressure to $20^{\circ} \mathrm{C} ?$ (c) How much work does the gas do in this process?

Ajay Singhal

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Problem 41

Diesel engines rely on compression to raise air in the cylinders to the fuel ignition temperature. In a particular diesel engine, $0.60 \mathrm{~L}$ of air initially at $293 \mathrm{~K}$ and 1 atm is compressed adiabatically to one-twentieth of its initial volume. Find (a) the final pressure, (b) the work done, and (c) the final temperature.

Ajay Singhal

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Problem 42

A piston-cylinder system contains 0.10 mole of ideal gas at $300 \mathrm{~K}$. (a) If the gas expands isothermally, does heat flow into the gas or out? (b) How much heat is required to expand the gas volume by a factor of $3 ?$

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Problem 43

A container of fixed size contains $8.0 \mathrm{~g}$ of helium at $273 \mathrm{~K}$. How much heat is required to double the gas temperature?

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Problem 44

Consider air to be a mixture of $80 \%$ nitrogen and $20 \%$ oxygen. How much work is required to raise the temperature of 1 mole of air by $1^{\circ} \mathrm{C}$ in an adiabatic process?

Narayan Hari

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Problem 45

You have an expandable container with 0.50 mole of oxygen gas at $273 \mathrm{~K}$ and 1 atm. (a) What's the gas volume? (b) If the gas expands adiabatically to twice this volume, find the final pressure and the work done.

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Problem 46

Undergoing adiabatic expansion, 2.0 moles of hydrogen gas $\left(\mathrm{H}_{2}\right)$ do $750 \mathrm{~J}$ of work. (a) Does the gas temperature increase or decrease? Why? (b) Find the temperature change.

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Problem 47

Consider the four-step process shown in Figure $P 14.47$. Find (a) the work done in each step and (b) the net work done over the cycle.

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Problem 48

Repeat the preceding problem if all the arrows are reversed.

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Problem 49

A gas is compressed along path AB in Figure P14.49.
(a) Does its internal energy increase or decrease in this process?
(b) Find the work done in this process.

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Problem 50

Consider the three-step cycle described by the complete triangle in Figure $\mathrm{P} 14.49 .$ (a) Is the net work done over the cycle positive or negative? Why? (b) Find the net work.

Ajay Singhal

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Problem 51

A high-performance gasoline engine has a compression ratio of 10: 1 , meaning that air entering the cylinders is compressed to one-tenth its volume as the piston rises. If air enters this engine's cylinders at $290 \mathrm{~K}$ and $1 \mathrm{~atm},$ find $(\mathrm{a})$ the pressure and $(\mathrm{b})$ the temperature of the air at full compression. Assume adiabatic compression.

Ajay Singhal

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Problem 52

The pressure on a sample of water is increased from 1 atm to 200 atm, reducing its volume by $1 \%$. (a) Draw the pressureversus-volume graph for this process. (b) Estimate the work required. (c) Assume that the process takes place quickly enough so that no heat flows out of the water. By how much does the water's temperature increase?

Manish Jain

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Problem 53

Food, heat, and work. A runner uses about 80 kcal of internal energy to run each kilometer. (a) If the runner loses $120 \mathrm{~g}$ of perspiration while running $1 \mathrm{~km},$ find the heat lost in the process. (b) How much work does the runner do in running that kilometer?

Ajay Singhal

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Problem 54

Heat and physical activity. In a bench press, a weight lifter lifts $125 \mathrm{~kg} 42 \mathrm{~cm} .$ In so doing, the athlete expends $1.3 \mathrm{~kJ} .$
(a) What's the heat flow involved in this process? (b) How many repetitions does the weight lifter need to make in order to "burn" 100 kcal?

Ajay Singhal

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Problem 55

Find the entropy change when water at $25^{\circ} \mathrm{C}$ (a) absorbs $1000 \mathrm{~J}$ of heat and (b) loses $1000 \mathrm{~J}$ of heat. Assume there's enough water that its temperature change is negligible.

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Problem 56

Find the entropy change when $75 \mathrm{~g}$ of steam condenses to water at $100^{\circ} \mathrm{C}$.

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Problem 57

Find the entropy created when $100 \mathrm{~g}$ of ice melts at $0^{\circ} \mathrm{C}$ Compare with the entropy created when the same mass of water boils at $100^{\circ} \mathrm{C}$.

Shahab Ullah

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Problem 58

Find the net entropy change when a $50-\mathrm{g}$ ice cube initially at $0^{\circ} \mathrm{C}$ melts in (a) a $10^{\circ} \mathrm{C}$ room and (b) a $35^{\circ} \mathrm{C}$ room.

Ajay Singhal

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Problem 59

$150 \mathrm{~g}$ of water at $0^{\circ} \mathrm{C}$ are placed in a freezer at $-4^{\circ} \mathrm{C}$. Find the net entropy change after all the water has turned to ice but is still at $0^{\circ} \mathrm{C}$.

Narayan Hari

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Problem 60

Using data from Chapter $13,$ find the entropy increase in $1.5 \mathrm{~kg}$ of mercury when it melts at $-39^{\circ} \mathrm{C}$ and 1 atm pressure.

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Problem 61

Using data from Chapter $13,$ find the entropy increase when $100 \mathrm{~g}$ of nitrogen boil at atmospheric pressure.

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Problem 62

Earth receives energy from the Sun at an average rate of about $240 \mathrm{~W} / \mathrm{m}^{2}$. Given Earth's average temperature of $15^{\circ} \mathrm{C}$, find the rate of entropy increase associated with this energy flow.

Narayan Hari

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Problem 63

A heat engine does $650 \mathrm{~J}$ of work and dumps $1270 \mathrm{~J}$ of heat to its cold reservoir. What's its efficiency?

Shahab Ullah

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Problem 64

A $40 \%$ efficient heat engine does mechanical work at the rate of $400 \mathrm{~W}$. If it runs for an entire day, find the heat removed from the hot reservoir and the heat transferred to the cold reservoir.

Shahab Ullah

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Problem 65

Each second a nuclear power plant extracts $1700 \mathrm{MJ}$ of thermal energy from its uranium fuel and dumps $1100 \mathrm{MJ}$ of waste heat into a river. (a) What's its efficiency? (b) At what rate does it produce electrical energy, assuming all the work it does ends up as electricity?

Shahab Ullah

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Problem 66

An automobile engine with an efficiency 0.21 dumps heat to the environment at the rate of $330 \mathrm{~kW}$. What's its mechanical power output, in $\mathrm{W}$ and in hp?

Shahab Ullah

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Problem 67

Find the maximum possible efficiency of a heat engine operating between the freezing and boiling points of water.

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Problem 68

Find the maximum temperature in a Carnot cycle operating in a room-temperature $\left(20^{\circ} \mathrm{C}\right)$ environment if its Carnot efficiency is 0.5

Shahab Ullah

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Problem 69

One alternative energy source is the temperature difference between surface and deep water in the tropical oceans. Suppose a heat engine uses $25^{\circ} \mathrm{C}$ surface water as its hot reservoir and $4^{\circ} \mathrm{C}$ deep water as its cold reservoir. (a) Find the maximum efficiency of such an engine.
(b) How much heat would have to be removed from the surface water each day in order to produce energy at the rate of a typical large power plant, about $1000 \mathrm{MW} ?$

Narayan Hari

Numerade Educator

Problem 70

A power plant produces electrical energy at the rate of 1300 MW with an efficiency of 0.31 . The excess heat is dumped into a river that carries $1500 \mathrm{~m}^{3} / \mathrm{s}$ of water. How much does the river's temperature increase?

Ajay Singhal

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Problem 71

A refrigerator with $\mathrm{COP}=3.8$ consumes electrical energy at the rate of $600 \mathrm{~W}$. At what rate can this refrigerator remove heat from its interior?

Shahab Ullah

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Problem 72

A window air conditioner consumes $1200 \mathrm{~W}$ of electric power and has $\mathrm{COP}=3.2$. If it runs continuously for $24 \mathrm{~h}$, how much heat gets removed from the house?

Shahab Ullah

Numerade Educator

Problem 73

Find the maximum possible COP for a refrigerator that liquefies nitrogen at $77 \mathrm{~K}$ in a lab at $22^{\circ} \mathrm{C}$.

Shahab Ullah

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Problem 74

Find the maximum possible COP for a freezer that maintains $-5^{\circ} \mathrm{C}$ when the surrounding room temperature is $25^{\circ} \mathrm{C}$

Shahab Ullah

Numerade Educator

Problem 75

Winter heating of an office building requires an average of $250 \mathrm{kBtu} / \mathrm{h}$. The heating system uses a heat pump with $\mathrm{COP}=$ 3.0
(a) If the energy supplied to the heat pump costs $\$ 0.09 / \mathrm{kWh}$ what's the cost per day to heat the building? (b) What's the daily monetary savings, compared with heat from oil at $\$ 4.20$ per gallon? The oil contains $40 \mathrm{kWh}$ per gallon and burns at $87 \%$ efficiency.

Manish Jain

Numerade Educator

Problem 76

Construct tables similar to Table 14.2 for (a) five and (b) six molecules.

Manish Jain

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Problem 77

For both cases in the preceding problem, show that the probabilities of all the macrostates sum to $1 .$

Manish Jain

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Problem 78

Compute the entropy of each macrostate in the gases of Problem 76.

Manish Jain

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Problem 79

For an $N$ -molecule gas, show that the number of microstates with $n$ molecules on the left side of the box is $N ! /[n !(N-n) !]$. Hint: Consider the pattern established by the cases of two, three, four, and five molecules.

Supratim Pal

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Problem 80

You flip a coin 50 times. (a) How many different microstates are there, counting as microstates each distinct ordering of heads and tails in the sequence? (b) Find the probability of getting heads 0 times, 10 times, 25 times, 40 times, and 50 times.

Supratim Pal

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Problem 81

A standard deck of cards contains 52 different cards. A poker hand consists of five cards, chosen randomly. How many different poker hands are there?

Supratim Pal

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Problem 82

In the game of poker (see the preceding problem), three of a kind (for example, three queens) beats two pair (for example, two aces and two fives). The better hand is the one with the lower probability. Show that three of a kind is less probable than two pair.

Supratim Pal

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Problem 83

An ideal gas expands 10 -fold in volume, maintaining a constant 440-K temperature. If the gas does $3.3 \mathrm{~kJ}$ of work,
(a) how much heat does it absorb and (b) how many moles of gas are there?

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Problem 84

It takes $600 \mathrm{~J}$ to compress a gas isothermally to half its initial volume. How much work would it take to compress it by a factor of 10 from its original volume?

Narayan Hari

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Problem 85

A gas undergoes an adiabatic compression that halves its volume. If its pressure increases by a factor of $2.55,$ what's the specific-heat ratio $\gamma ?$

Narayan Hari

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Problem 87

Repeat the preceding problem if $\mathrm{AB}$ is an adiabat and $\gamma=1.4$

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Problem 88

The McNeil Generating Station in Burlington, Vermont is one of the world's largest wood-fired electric power plants. The plant produces steam at $950^{\circ} \mathrm{F}$ to drive its turbines, and condensed steam returns to the boiler at $90^{\circ} \mathrm{F}$. (Note the temperatures in Fahrenheit, used in U.S. engineering situations.) Find McNeil's maximum thermodynamic efficiency and compare with its actual efficiency of $25 \% .$ Note: Some of the difference comes from having to evaporate moisture out of the wood-chip fuel.

Ajay Singhal

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Problem 89

A nuclear power plant has a maximum steam temperature $\left(T_{\mathrm{H}}\right)$ of $310^{\circ} \mathrm{C}$. It produces $650 \mathrm{MW}$ of electric power in the winter, when its $T_{\mathrm{C}}$ is effectively $0^{\circ} \mathrm{C}$.
(a) Find its maximum winter efficiency. (b) If its summertime $T_{\mathrm{C}}$ is $38^{\circ} \mathrm{C},$ what's its summertime electric power output, assuming nothing else changes?

Shahab Ullah

Numerade Educator

Problem 90

Blood flow. As the heart beats, blood pressure in an artery varies from $80 \mathrm{~mm} \mathrm{Hg}$ to $125 \mathrm{~mm}$ Hg (gauge pressures). An air bubble trapped in the artery has a diameter of $1.52 \mathrm{~mm}$ at the minimum pressure. (a) What will its diameter be at the maximum pressure? (b) How much work does the blood (and ultimately the heart) do in compressing the bubble? Assume a constant $37^{\circ} \mathrm{C}$ temperature.

Supratim Pal

Numerade Educator

Problem 91

A gas with $\gamma=1.4$ occupies $5.0 \mathrm{~L}$ at $100 \mathrm{kPa}$ pressure.
(a) What's the gas's final pressure?
(b) How much work is needed to compress the gas adiabatically to $2.5 \mathrm{~L} ?$

Ajay Singhal

Numerade Educator

Problem 92

Two moles of ideal gas with molar specific heat $c_{\mathrm{V}}=\frac{5}{2} R$ are at $T=300 \mathrm{~K}$ and $P=100 \mathrm{kPa}$. Determine the final temperature and the work done on the gas when $1.5 \mathrm{~kJ}$ of heat is added (a) isothermally, (b) at constant volume, and (c) at constant pressure.

Supratim Pal

Numerade Educator

Problem 93

Warm winds called Chinooks sweep across the plains just east of the Rocky Mountains. They carry air from high in the mountains down to the plains so fast that the air has no time to exchange significant heat with its surroundings (Figure GP1 4.93). On the day of a Chinook, pressure and temperature high in the Alberta Rockies are $62.0 \mathrm{kPa}$ and $-11.0^{\circ} \mathrm{C},$ respectively.
(a) What will the air temperature be once it's reached the city of Calgary, where the pressure is $86.5 \mathrm{kPa}$ ? (b) How much work is done on what was initially a cubic meter of air as it descends to the plain?

Supratim Pal

Numerade Educator

Problem 94

It costs $\$ 180$ to heat a home with electricity in a typical winter month. (An electric furnace converts all the electrical energy to heat.) What's the monthly heating bill following conversion to an electrically powered heat pump with $\mathrm{COP}=3.1 ?$

Narayan Hari

Numerade Educator

Problem 95

A 4.0 - $L$ sample of water at $9.0^{\circ} \mathrm{C}$ is put into a refrigerator. The refrigerator's 130 -W motor runs for 4.0 min to cool the water to the refrigerator's low temperature of $1.0^{\circ} \mathrm{C}$. (a) What's the COP of the refrigerator? How does this compare with the maximum possible COP if the refrigerator exhausts heat to the kitchen at $25^{\circ} \mathrm{C} ?$

Ajay Singhal

Numerade Educator

Problem 96

A jet aircraft engine is a gas turbine, using hot combustion gases directly to spin a turbine. Gas turbines operate at high temperatures $\left(T_{\mathrm{H}}\right),$ but they aren't very efficient because their exhaust temperature $\left(T_{\mathrm{C}}\right)$ is also high. Find the maximum possible efficiency of a gas turbine operating between $1050^{\circ} \mathrm{C}$ and $590^{\circ} \mathrm{C}$

Narayan Hari

Numerade Educator

Problem 97

Despite its inefficiency, the gas turbine enables our most efficient fossil-fueled power plant, the combined-cycle gas turbine. This system burns natural gas in a gas turbine, then uses the turbine's exhaust to drive a conventional steam cycle. Consider a system using the gas turbine of the preceding problem, with the steam cycle then operating between the turbine's $590^{\circ} \mathrm{C}$ exhaust and discharging waste heat at $42^{\circ} \mathrm{C}$. Find (a) the maximum efficiency of the steam cycle alone and (b) the maximum efficiency of the combined cycle.

Ajay Singhal

Numerade Educator

Problem 98

Human entropy production. An athlete with a daily food intake of 2800 kcal uses only about $25 \%$ of that energy for vital body functions, with the rest lost as heat. The heat is conducted from the body's core at $37^{\circ} \mathrm{C}$ to the outer skin, which has an average temperature of $30^{\circ} \mathrm{C}$. (a) How much entropy is produced each day in this process? (b) How much additional entropy is produced when the heat is radiated away to the surrounding air, at $20^{\circ} \mathrm{C} ?$

Supratim Pal

Numerade Educator

Problem 99

An ideal gas with $\gamma=5 / 3$ starts at point A in Figure GP1 $4.99,$ where its volume and pressure are $1.00 \mathrm{~m}^{3}$ and 250 kPa, respectively. It undergoes adiabatic expansion that triples its volume, ending at point B. It's then heated at constant volume to point $\mathrm{C},$ and finally is compressed isothermally back to point $\mathrm{A}$. Find (a) the pressure of the gas at $\mathrm{B},$ (b) the pressure at $\mathrm{C},$ and
(c) the net work done on the gas.

Manish Jain

Numerade Educator