Deck 14: Second Law of Thermodynamics

Question 1

A thermodynamic engine absorbs 64 kcal of energy each cycle and exhausts 42 kcal.
(a)What is the efficiency of this engine?
(b)How much work does this engine do per cycle?

Answer 1

(a)34%
(b)22 kcal

Question 2

A thermodynamic engine receives 7000 J of energy and loses 3000 J in each cycle.What is the efficiency of this engine?

A)57%
B)30%
C)70%
D)43%

Answer 2

A

Question 3

The figure shows a pV diagram for a cycle of a thermodynamic engine for which Q_H = 59 J.What is the thermal efficiency of the engine?

A)17%
B)34%
C)8.5%
D)14%

Answer 3

A

Question 4

If the efficiency of a Carnot engine were to be 100%,the cool reservoirs would have to be

A)at absolute zero.
B)at 0°C.
C)at 100°C.
D)infinitely hot.

Question 5

An ideal Carnot thermodynamic engine operates between reservoirs at 1740 K and In each cycle,260 J of thermal energy is rejected to the low temperature reservoir.In each cycle,how much mechanical work W is performed by the engine?

Question 6

An ideal gas undergoes an isothermal expansion.During this process,its entropy

A)decreases.
B)remains unchanged.
C)increases.
D)cannot be predicted from the data given.

Question 7

An important feature of the Carnot cycle is that

A)its efficiency can be 100%.
B)its efficiency depends only on the absolute temperature of the hot reservoir used.
C)its efficiency is determined by the temperatures of the hot and cold reservoirs between which it works and by the properties of the working substance used, and on nothing else.
D)it is an example of an irreversible process that can be analyzed exactly without approximations.
E)no engine can be more efficient than a Carnot engine operating between the same two temperatures.

Question 8

A thermodynamic engine has an efficiency of 35.0% and receives 150 J of energy per cycle.
(a)How much work does it do in each cycle?
(b)How much thermal energy does it "waste" in each cycle?

Question 9

A certain thermodynamic engine extracts 1.30 kJ of thermal energy from a hot temperature reservoir and discharges 0.70 kJ of energy to a cold temperature reservoir.What is the efficiency of this engine?

A)46%
B)54%
C)86%
D)27%
E)13%

Question 10

A nuclear power plant has an actual efficiency of 33%.If of energy are released from fission,how much electric power does the power plant produce?

A)0.063 MW
B)6.3 MW
C)25 MW
D)0.25 MW

Question 11

A gas follows the pV trajectory shown in Figure 16.2.How much work is done per cycle by the gas if the gas in a thermodynamic engine follows the cycle shown in the pV diagram.How much work does this engine do each cycle if p₀ =

A)220 J
B)440 J
C)870 J
D)1100 J

Question 12

A certain automobile engine takes in 4.00 kJ of energy and performs 1.10 kJ of mechanical work in each cycle.
(a)Calculate the engine's efficiency.
(b)How much thermal energy is "wasted" in each cycle?

Question 13

Which of the following is a false statement?

A)Entropy is a quantitative measure of disorder.
B)The total entropy change in one cycle of a Carnot engine is zero.
C)The entropy of an isolated system remains constant.
D)Entropy can be measured in units of J/K.

Question 14

Which one of the following is a true statement?

A)The second law of thermodynamics is a consequence of the first law of thermodynamics.
B)It is possible for thermal energy to flow spontaneously from a hot body to a cold one or from a cold one to a hot one, depending on whether or not the process is reversible or irreversible.
C)It is not possible to convert work entirely into thermal energy.
D)It is impossible to transfer thermal energy from a cooler to a hotter body.
E)All of these statements are false.

Question 15

An ideal Carnot engine is operated between a hot and a cold reservoir.The temperature difference between the two reservoirs is 284°C.If the efficiency of this ideal engine is 24.0%,find the temperature of the cold reservoir in degrees Celsius.

Question 16

A thermodynamic engine with an efficiency of 30% performs 2500 J of work.How much thermal energy is discharged to the lower temperature reservoir?

A)5800 J
B)8300 J
C)750 J
D)1400 J
E)7100 J

Question 17

When water at 0°C freezes,the entropy of the water

A)increases.
B)decreases.
C)remains constant.
D)could either increase or decrease; it depends on other factors.

Question 18

A thermodynamic engine absorbs 85.6 kJ of energy each cycle and exhausts 61.8 kJ.
(a)What is the efficiency of the engine?
(b)How much work does it do each cycle?

Question 19

A thermodynamic engine has an efficiency of 31.4% and receives 8.72 kJ of energy per cycle.
(a)How much work does it perform in each cycle?
(b)How much energy does it exhaust in each cycle?

Question 20

During each cycle,a thermodynamic engine takes in 4.0 J of energy,does 1.0 J of work,and expels 3.0 J of energy.What is its efficiency?

Question 21

What is the efficiency of an ideal Carnot engine operating between a reservoir in which ice and water coexist,and a reservoir in which water and steam coexist? The pressure is constant at 1.0 atm for both reservoirs.

A)27%
B)0.27%
C)100%
D)1.0%
E)15%

Question 22

For a certain ideal Carnot engine,the hot reservoir is 35 C° higher than the cold reservoir.If this engine is to have an efficiency of 20%,what must be the temperature of the hot reservoir?

A)70.0 K
B)140 K
C)175 K
D)210 K
E)245 K

Question 23

Two ideal Carnot thermodynamic engines have the same efficiency.One operates between 5.0 × 10² K and 3.0 × 10² K,and the other between 4.0 × 10² K and some lower temperature.What is the lower temperature?

A)200 K
B)220 K
C)240 K
D)260 K
E)280 K

Question 24

An inventor tries to sell you his new thermodynamic engine that takes in 40 J of energy at 87°C on each cycle,expels 30 J at 27°C,and does 10 J of work.Would it be wise to invest in this engine? Back up your conclusion with numerical calculations.

Question 25

One of the most efficient engines built so far has the following characteristics: The combustion chamber temperature is 1900°C,the exhaust temperature = 430°C,7.0 × 10⁹ cal of fuel produces 1.4 × 10¹⁰ J of work in one hour.(1 cal = 4.186 J)
(a)What is the actual efficiency of this engine?
(b)What is the power output of this engine?
(c)What would be the maximum possible efficiency for an engine using the same temperature extremes?

Question 26

A real (non-Carnot)thermodynamic engine,operating between thermal energy reservoirs at temperatures of 450 K and 270 K,performs 3.3 kJ of net work,and rejects 8.2 kJ of energy in a single cycle.
(a)What is the thermal efficiency of this thermodynamic engine?
(b)What is the maximum efficiency it could possibly have?

Question 27

An ideal Carnot engine has an efficiency of 83.0% and performs 4500 J of work every cycle.How much energy is discharged to the lower temperature reservoir every cycle?

A)920 J
B)830 J
C)740 J
D)3700 J
E)5400 J

Question 28

An ideal Carnot engine operating between a warm reservoir of unknown temperature and a cold reservoir at has an efficiency of What is the temperature of the warm reservoir?

A)1.98 K
B)0.180 K
C)157 K
D)0.160 K

Question 29

An ideal Carnot engine operates between a high temperature reservoir at and a river with water at If it absorbs of energy each cycle,how much work per cycle does it perform?

A)1642 J
B)2358 J
C)1483 J
D)2517 J

Question 30

A thermodynamic engine having the maximum possible efficiency has an efficiency of 25% when operating between two heat reservoirs.If the temperature of the cold reservoir is 300 K,what is the temperature of the hot reservoir?

A)350 K
B)375 K
C)400 K
D)450 K
E)500 K

Question 31

A thermodynamic engine having the maximum possible efficiency has an efficiency of 35.0% when operating between two heat reservoirs.If the temperature of the hot reservoir is 700 K,what is the temperature of the cold reservoir?

A)200 K
B)245 K
C)350 K
D)455 K
E)600 K

Question 32

A Carnot engine operates between two reservoirs with unknown temperatures.If the Carnot engine operates at efficiency,what is the ratio of the absolute temperatures of the reservoirs,T_c/T_h?

A)0.33
B)0.0012
C)0.0025
D)0.67

Question 33

The "hot shot" thermodynamic engine operating between 40°C and 380°C has an efficiency that is 60% of that of an ideal Carnot engine operating between the same temperatures.If the "hot shot" engine absorbs energy at a rate of 60 kW,at what rate does it exhaust energy?

A)36 kW
B)41 kW
C)57 kW
D)60 kW

Question 34

The ocean thermal energy conversion project uses the surface water near tropical islands with a temperature of 20°C as the hot temperature reservoir,and the water at some depth,with a temperature of 5.0°C,as the cold temperature reservoir for a thermodynamic engine.What is the maximum possible efficiency of an engine running between those two temperatures?

A)4.7%
B)5.1%
C)7.9%
D)15%
E)30%

Question 35

A coal-fired plant generates 600 MW of electric power.The plant uses 4.8 × 10⁶ kg of coal each day,and the heat of combustion of coal is 3.3 × 10⁷ J/kg.The steam that drives the turbines is at a temperature of 300°C,and the exhaust water is at 37°C.
(a)What is the overall efficiency of the plant for generating electric power?
(b)How much thermal energy is exhausted each day?
(c)Using the same heat reservoirs,what is the maximum possible efficiency for a thermodynamic engine?

Question 36

An ideal Carnot thermodynamic engine has an efficiency of 0.600.If it operates between a deep lake with a constant temperature of and a hot reservoir,what is the temperature of the hot reservoir?

A)735 K
B)490 K
C)470 K
D)784 K

Question 37

An ideal Carnot thermodynamic engine operates between and What is its efficiency?

A)0.38
B)0.62
C)0.61
D)1.61

Question 38

An ideal Carnot engine operating between a warm reservoir of unknown temperature and a cold reservoir at has an efficiency of What is the temperature of the warm reservoir?

A)2.93 K
B)0.0500 K
C)106 K
D)0.0400 K

Question 39

An ideal Carnot engine operates between a warm reservoir at 233 K and a colder reservoir.During each cycle,this engine extracts of energy from the warm reservoir and does of work.What is the temperature of the colder reservoir?

A)171 K
B)62 K
C)47 K
D)67 K

Question 40

An ideal Carnot engine extracts 529 J of energy from a high-temperature reservoir during each cycle,and rejects of energy to a low-temperature reservoir during the same cycle.What is the efficiency of the engine?

A)0.57
B)1.35
C)2.35
D)0.7

Question 41

An ideal Carnot air conditioner operates between an indoor temperature of 20°C and an outdoor temperature of 39°C.How much energy does it use to remove 2000 J of thermal energy from the interior of the house?

A)105 J
B)130 J
C)780 J
D)520 J
E)340 J

Question 42

A reversible engine takes in energy at a rate of 555 W and exhausts energy at 482 W.
(a)How much power does it produce?
(b)What is its efficiency?
(c)If operated in reverse as a refrigerator,what would be its performance coefficient (COP)?

Question 43

During each cycle,the compressor in a certain ideal Carnot refrigerator performs 480 J of work to remove 150 J of thermal energy from the interior of the refrigerator.How much thermal energy do the coils behind the refrigerator discharge into the kitchen each cycle?

A)110 J
B)150 J
C)330 J
D)480 J
E)630 J

Question 44

A refrigerator has a performance coefficient (COP)of 1.15,and it extracts 7.95 J of energy from the cold reservoir during each cycle.
(a)How much work is done on the gas in each cycle?
(b)How much energy is exhausted into the hot reservoir in each cycle?

Question 45

A thermodynamic pump absorbs thermal energy from the atmosphere at a rate of 30 kW.If work is being done to run this thermodynamic pump at a rate of 7.7 kW,what is the coefficient of performance (COP)of the thermodynamic pump?

A)3.9
B)4.9
C)2.9
D)0.26
E)22

Question 46

A Carnot air conditioner has a coefficient of performance of 17.0 and removes 72.0 MJ of thermal energy from the interior of a house every hour.How much power does it consume?

A)1180 W
B)1320 W
C)520 kW
D)3.14 MW
E)1.25 MW

Question 47

What is the change in entropy when 15.0 g of water at 100°C are turned into steam at 100°C? The latent heat of vaporization of water is 22.6 × 10⁵ J/kg.

A)90.8 J/K
B)-90.8 J/K
C)339 J/K
D)-339 J/K
E)0 J/K

Question 48

A 15.0-kg block of ice at 0.00°C falls into Lake Superior,which is a fresh water lake.The lake water is at 10.0°C,and the latent heat of fusion for ice is 3.34 × 10⁵ J/kg.Find the change in entropy due to the melting of the ice (a)of the block of ice,(b)of the lake,and (c)of the system consisting of the lake and the ice.(d)Is your answer to part (c)consistent with the reversibility or irreversibility of the melting process?

Question 49

During each cycle of operation,a refrigerator absorbs 230 J of energy from the freezer and expels 356 J of energy to the room.How much work input is required in each cycle?

A)712 J
B)586 J
C)460 J
D)126 J

Question 50

An air conditioner with a coefficient of performance of 3.50 uses 30.0 kW of power to operate.What power is it discharging to the outdoors?

A)30.0 kW
B)75.0 kW
C)105 kW
D)135 kW
E)210 kW

Question 51

An ideal Carnot engine is operated as a thermodynamic pump to heat a room in the winter.The thermodynamic pump delivers thermal energy to the room at the rate of 47 kJ per second and maintains the room at a temperature of 293 K when the outside temperature is 237 K.The power requirement to run the thermodynamic pump under these operating conditions is closest to

A)9000 W.
B)7100 W.
C)20,000 W.
D)15,000 W.
E)11,000 W.

Question 52

Suppose that the Department of Energy develops a new reversible engine that has a coefficient of performance (COP)of 4.0 when operated as a refrigerator and a COP of 5.0 when operated as a thermodynamic pump.What is its thermal efficiency when operated as a thermodynamic engine doing work?

A)10%
B)20%
C)25%
D)45%
E)80%

Question 53

An ideal Carnot refrigerator powered from an electrical outlet takes heat from water at 0.0°C and rejects energy to a room at How much electrical energy must be supplied to the refrigerator so it will convert 78 g of water at 0.0°C to ice at 0.0°C.The latent heat of fusion of water is 3.34 × 10⁵ J/kg.

Question 54

During each cycle,a refrigerator removes 20.0 kJ of heat from the freezing compartment and ejects 24.0 kJ into a room.
(a)How much work per cycle is required each cycle to run this refrigerator?
(b)What is the coefficient of performance of this refrigerator?

Question 55

An ideal Carnot engine is operated as an air conditioner to cool a house in the summer.The air conditioner removes of thermal energy per second from the house,and maintains the inside temperature at while the outside temperature is The power required to run the air conditioner under these operating conditions is closest to

A)3600 W.
B)4400 W.
C)5100 W.
D)5800 W.
E)6600 W.

Question 56

If the efficiency of a reversible engine is 28%,what is its COP (performance coefficient)operated (a)as a refrigerator,and (b)as a thermodynamic pump?

Question 57

An ideal reversible thermodynamic pump is taking heat from the outside air at -10.0°C and discharging it into the house at 18.0°C.What is the coefficient of performance of this thermodynamic pump?

A)10.4
B)9.44
C)0.644
D)0.533
E)0.0962

Question 58

A thermodynamic pump with a performance coefficient (COP)of 4.9 absorbs thermal energy from the atmosphere at a rate of At what rate is work being done to run this thermodynamic pump?

A)6 kW
B)142 kW
C)113 kW
D)35 kW

Question 59

A refrigerator has a coefficient of performance equal to 4.2.How much work must be done on the operating gas in the refrigerator in order to remove 250 J of energy from the interior compartment?

A)60 J
B)120 J
C)250 J
D)480 J
E)1050 J

Question 60

An ideal Carnot refrigerator with a performance coefficient (COP)of 5.0 cools items inside of it to What is the high temperature needed to operate this refrigerator?

A)61° C
B)1395° C
C)6° C
D)30° C

Question 61

When 1.0 kg of steam at 100°C condenses to water at 100°C,what is the change in entropy of the steam? The latent heat of vaporization of water is 22.6 × 10⁵ J/kg.

A)zero
B)6.1 × 10³ J/K
C)-6.1 × 10³ J/K
D)22.6 × 10⁵ J/K
E)-22.6 × 10⁵ J/K

Question 62

What is the change in entropy of the ice when a 0.050-kg ice cube at 0°C melts? The latent heat of fusion for water is 80 cal/g.

Question 63

When 0.50 kg of water at 0°C freezes,what is the change in entropy of the water? The latent heat of fusion of water is 33,400 J/kg.

A)0 J/K
B)610 J/K
C)-610 J/K
D)-17,000 J/K
E)17,000 J/K

Question 64

What is the entropy change of 450 g of water when it changes from (a)liquid to steam at its usual boiling point and (b)ice to liquid at its usual melting point? For water,L_F = 0.334 MJ/kg,L_V = 2.26 MJ/kg.

Question 65

On a cold winter day,the outside temperature is -20°C and the inside temperature is maintained at 20°C.There is a net thermal energy flow to the outside through the walls,roof,etc.,of 25 kW.What is the rate of increase of the entropy of the universe as a result of this energy flow?

A)13 W/K
B)25 W/K
C)85 W/K
D)99 W/K
E)0 W/K

Question 66

A 0.42-kg quantity of ethanol,in the liquid state at its melting point of -114.4°C,is frozen at atmospheric pressure.The heat of fusion of ethanol is 1.04 × 10⁵ J/kg,and its molecular mass is 46.1 g/mol.What is the change in the entropy of the ethanol as it freezes?

A)-280 J/K
B)-250 J/K
C)-310 J/K
D)250 J/K
E)280 J/K

Question 67

What is the change in entropy of the lead when 2.0 kg of molten lead at its melting point temperature solidifies? For lead: L_V = 207 kcal/kg at 1744°C,L_F = 5.9 kcal/kg at 328°C.

Question 68

A container of ideal gas at STP undergoes an isothermal expansion and its entropy changes by 3.7 J/K.How much work does it do?

A)0.0 J
B)1.0 × 10³ J
C)-1.0 × 10³ J
D)1.4 × 10³ J
E)-1.4 × 10³ J

Question 69

An irreversible engine operating between the temperatures of 550 K and 300 K extracts 1.20 kJ of thermal energy from the hot reservoir and produces 0.450 kJ of work.How much entropy is created in the process?

A)0.32 J/K
B)0.68 J/K
C)0.44 J/K
D)0.73 J/K
E)0 J/K

Question 70

On a cold winter day,the outside temperature is -20°C and the inside temperature is maintained at 20°C.There is a net thermal energy flow to the outside through the walls,roof,etc.,of 25 kW.At what rate is the entropy of the air outside the house changing as a result of this process?

A)+13 W/K
B)-25 W/K
C)85 W/K
D)+99 W/K
E)0 W/K