Deck 20: The Second Law of Thermodynamics

Question 1

The efficiency of an engine

A)can have units of Joules.
B)is always less than 100%.
C)is the ratio of the work done by the engine to the heat exhausted to the low temperature reservoir.
D)is the ratio of the heat exhausted to the low temperature reservoir to the work done by the engine.

Answer 1

is always less than 100%.

Question 2

One end of a metal rod is in contact with a reservoir at a 400K and the other end in contact with a reservoir at 100K.The rod and reservoirs make up a closed system.If 5500 J are conducted from one end to the other uniformly (no change in temperature along the rod)what is the change in entropy of the system?

A)8.56 J/K
B)10.9 J/K
C)25.4 J/K
D)41.3 J/K
E)68.8 J/K

Answer 2

41.3 J/K

Question 3

An engine exhausts 600 J of of heat to the cold temperature reservoir and has an efficiency of 25%.How much work is done by the engine?

A)200 J
B)800 J
C)650 J
D)400 J

Answer 3

200 J

Question 4

A refrigerator has a coefficient of performance of 6.If the refrigerator absorbs 50 cal of heat from the cold reservoir in each cycle,evaluate the heat expelled into the heat reservoir.

A)40 cal
B)48 cal
C)50 cal
D)58 cal
E)60 cal

Question 5

A Carnot engine uses reservoirs at temperatures of 27.0 ^$\circ$ C and 327 ^$\circ$ C.In one cycle,it uses 1200 J of heat from the high temperature reservoir.How much heat is exhausted to the low temperature reservoir in one cycle?

A)300 J
B)354 J
C)550 J
D)600 J

Question 6

An engine exhausts 600 J of of heat to the cold temperature reservoir and has an efficiency of 25%.How much heat does it take in from the high temperature reservoir?

A)800 J
B)650 J
C)400 J
D)2400 J

Question 7

One end of a metal rod is in contact with a reservoir at a 400 K and the other end in contact with a reservoir at 200 K.The rod and reservoirs make up a closed system.If 5500 J are conducted from one end to the other uniformly (no change in temperature along the rod)what is the change in entropy of the 200 K reservoir?

A)27.5 J/K
B)10.5 J/K
C)13.8 J/K
D)0.00 J/K
E)8.56 J/K

Question 8

A heat pump has a coefficient of performance of 6.If the heat pump absorbs 50 cal of heat from the cold outdoors in each cycle.Evaluate the heat expelled to the warm indoors.

A)40 cal
B)48 cal
C)50 cal
D)58 cal
E)60 cal

Question 9

How much work will need to be input to extract 5.0 J of heat from the cold reservoir of a Carnot refrigerator operated between 20 ^$\circ$ C and 0 ^$\circ$ C?

A)0.23 J
B)0.37 J
C)0.56 J
D)0.68 J
E)0.71 J

Question 10

How much work will need to be input to expel 5.0 J of heat to the hot reservoir of a Carnot heat pump operated between 20 ^$\circ$ C and 0 ^$\circ$ C?

A)0.23 J
B)0.37 J
C)0.56 J
D)0.68 J
E)0.34 J

Question 11

An engine takes in 600 J of heat from the high temperature reservoir and has an efficiency of 25%.How much heat does it exhaust to the cold reservoir?

A)400 J
B)150 J
C)200 J
D)650 J

Question 12

Two six-sided dice are rolled and the two numbers are added together.What is the probability of getting a total of seven?

A)1/36
B)1/12
C)1/6
D)7/12

Question 13

A Carnot engine uses reservoirs at temperatures of 27.0 ^$\circ$ C and 327 ^$\circ$ C.In one cycle,it uses 600 J of heat from the high temperature reservoir.How much work does it do in one cycle?

A)300 J
B)354 J
C)550 J
D)600 J

Question 14

If 5.0 J of heat are extracted from the cold reservoir of a Carnot refrigerator operated between 20 ^$\circ$ C and 0 ^$\circ$ C,how much heat is expelled into the hot reservoir?

A)4.66 J
B)2.02 J
C)5.37 J
D)3.23 J
E)0.71 J

Question 15

One end of a metal rod is in contact with a reservoir at a 400 K and the other end in contact with a reservoir at 100 K.The rod and reservoirs make up a closed system.If 5500 J are conducted from one end to the other uniformly (no change in temperature along the rod)what is the change in entropy of the rod?

A)0.0 J/K
B)18.3 J/K
C)21.1 J/K
D)34.4 J/K
E)37.2 J/K

Question 16

An engine takes in 600 J of heat from the high temperature reservoir and exhausts 400 J to the low temperature reservoir.What is the efficiency of this engine?

A)25.0%
B)33.3%
C)40.0%
D)60.0%

Question 17

A solid mass of aluminum is at its melting point.During the melting process,the change in entropy of the aluminum is 9.11 * 10^-3 kJ/K.What is the mass of the aluminum?

A)20.0 g
B)28.9 g
C)23.7 g
D)21.4 g
E)26.3 g

Question 18

A solid 20.0-g mass of aluminum is at its melting point.What is the change in entropy the mass in the process of melting?

A)3.24 * 10^-3 kJ/K
B)4.58 * 10^-3 kJ/K
C)6.15 * 10^-3 kJ/K
D)8.50 * 10^-3 kJ/K
E)9.11 * 10^-3 kJ/K

Question 19

One end of a metal rod is in contact with a reservoir at a 400 K and the other end in contact with a reservoir at 100 K.The rod and reservoirs make up a closed system.If 5500 J are conducted from one end to the other uniformly (no change in temperature along the rod)what is the change in entropy of the 400 K reservoir?

A)10.5 J/K
B)8.56 J/K
C)0.00 J/K
D)-11.8 J/K
E)-13.8 J/K

Question 20

An engine takes in 600 J of heat from the high temperature reservoir and exhausts 400 J to the low temperature reservoir.What is the work done by this engine?

A)1000 J
B)200 J
C)400 J
D)700 J

Question 21

Burning of fuel transfers 4 * 10⁵ W of power into the engine of a 2000-kg vehicle;supposing that the engine is 25% efficient,determine the maximum speed the vehicle can achieve 5 seconds after starting from rest.

A)32.6 m/s
B)10.5 m/s
C)22.4 m/s
D)5.8 m/s
E)16.4 m/s

Question 22

The change in entropy of a system depends only on the initial and final states.This means that

A)the change in entropy for any process can be calculated.
B)any process is reversible.
C)entropy always increases.
D)All are correct.
E)None are correct.

Question 23

A coin is tossed five times.What is the probability that the coin lands four times heads up and once as tails?

A)0.031
B)0.082
C)0.16
D)0.25
E)0.31

Question 24

An outboard motor for a boat is cooled by the lake water at 15 ^$\circ$ C with a compression ratio of 10.Assume that the air is a diatomic gas.Calculate the efficiency of the Otto cycle.

A)30%
B)40%
C)50%
D)60%
E)70%

Question 25

A 0.750-kg iron bar is taken from a forge at 900 ^$\circ$ C and dropped into 14.00 kg of water at 20.0 ^$\circ$ C.Assuming that no energy is lost by heat to the surroundings as the water/iron reaches their final temperature,determine the total entropy change of the iron bar plus-water system.Assume that specific heat of iron is 448 J/(kg.K).

A)371 J/K
B)444 J/K
C)534 J/K
D)622 J/K
E)756 J/K

Question 26

A scientist looking at a very small,isolated,system observes that the entropy of the system spontaneously decreases while he is looking at it.If true,is this a Nobel-winning discovery or is this not that significant?

A)Yes.
B)No.entropy naturally tends to decrease with time.
C)No,such fluctuations are allowed in small systems.

Question 27

A water cooled engine produces 1000 W of power.Water enters the engine block at 15 ^$\circ$ C and exits at 30 ^$\circ$ C.The rate of water flow is 100 L/hr.What is the engine's thermal efficiency?

A)63.6%
B)36.4%
C)50%
D)10%
E)15%

Question 28

A 1.00-kg iron bar is taken from a forge at 800 ^$\circ$ C and dropped into 20.00 kg of water at 15.0 ^$\circ$ C.Assuming that no energy is lost by heat to the surroundings as the water/iron reaches their final temperature,determine the total entropy change of the iron bar plus-water system.Assume that specific heat of iron is 448 J/(kg.K).

A)371 J/K
B)444 J/K
C)534 J/K
D)622 J/K
E)756 J/K

Question 29

A 0.750-kg iron bar is taken from a forge at 900 ^$\circ$ C and dropped into 14.00 kg of water at 20.0 ^$\circ$ C.Assuming that no energy is lost by heat to the surroundings as the water/iron reaches their final temperature,determine the total entropy change of the water.Assume that specific heat of iron is 448 J/(kg.K).

A)-444 J/K
B)-614 J/K
C)-756 J/K
D)-534J/K
E)444 J/K

Question 30

Electrons have a property called spin that can either be up or down,analogous to how a coin can be heads or tails.Consider 6 electrons.Calculate the entropy for the case where four spins are up and two are down.

A)1.4 * 10^-23 J/K
B)2.2 * 10^-23 J/K
C)1.1 * 10^-23 J/K
D)4.6 * 10^-23 J/K
E)3.7 * 10^-23 J/K

Question 31

A refrigerator with a coefficient of performance of 3.6 is used to cool 3 liters of mineral water from room temperature (20 ^$\circ$ C)to 3 ^$\circ$ C.If the refrigerator runs at 525 W,how long will it take the water to reach 3 ^$\circ$ C? Recall that the heat capacity of water is 4.19 kJ/(kg K)and the density is 1 g/cm³.Assume the other contents of the refrigerator are already at 3C.

A)43 s
B)113 s
C)407 s
D)68 s
E)26 s

Question 32

Imagine dividing a box into two equal parts,part A on the left and part B on the right.Four identical gas atoms,numbered 1 through 4,are placed in the box.How many distinct microscopic states result in two of the atoms being in part A and the other two atoms in part B?

A)4
B)6
C)12
D)16
E)24

Question 33

If a power plant produces steam at 600 ^$\circ$ C and outputs heat at 150 ^$\circ$ C to a cogeneration power plant that then outputs its exhaust at a temperature of 40 ^$\circ$ C.Find the total efficiency of this combination of power plants.Assume both plants are 80% as efficient as a Carnot heat engine.

A)5.9%
B)47%
C)51%
D)53%
E)64%

Question 34

A 0.750-kg iron bar is taken from a forge at 900 ^$\circ$ C and dropped into 14.00 kg of water at 20.0 ^$\circ$ C.Assuming that no energy is lost by heat to the surroundings as the water/iron reaches their final temperature,determine the total entropy change of the water.Assume that specific heat of iron is 448 J/(kg.K).

A)444 J/K
B)534 J/K
C)756 J/K
D)622 J/K
E)995 J/K

Question 35

A refrigerator has a coefficient of performance of 4.2.If the refrigerator absorbs 55 cal of heat from the cold reservoir (kept at 4 ^$\circ$ C)in each cycle,evaluate the heat expelled into the heat reservoir (kept at 21 ^$\circ$ C).

A)13 cal
B)16 cal
C)61 cal
D)68 cal
E)71 cal

Question 36

Six coins are flipped simultaneously.Calculate the change in entropy of this system in units of k_B if another coin is added.

A)0.5
B)2.0
C)1.0
D)0.7
E)0.8

Question 37

An engine operates with an efficiency of 0.5.Which of the following temperatures cannot represent the temperatures of the hot and the cold reservoirs be respectively?

A)T_H = 600 K and T_C = 100
B)T_H = 600 K and T_C = 200
C)T_H = 500 K and T_C = 200
D)T_H = 500 K and T_C = 300

Question 38

What is the maximum possible efficiency for a heat engine moving heat from temperature of 670 ^$\circ$ C to a region of 25 ^$\circ$ C?

A)3.7%
B)32%
C)55%
D)68%
E)96%

Question 39

A nuclear submarine uses its reactor to heat water/steam to a temperature of 950 ^$\circ$ C.The steam drives turbines that turn the submarines propellers.After the steam passes through the turbines it is cooled to 4 ^$\circ$ C and condensed by the seawater that surrounds the submarine and returned to be heated by the reactor again.What is the upper limit of the efficiency of the submarine's turbines?

A)21.7%
B)38.6%
C)77.4%
D)85.1%
E)99.6%

Question 40

Find the ratio of the coefficients of performance for two ideal heat pumps used as heaters for a house.The house is kept at 21 ^$\circ$ C in both cases.In case 1 the outside temperature is 4.0 ^$\circ$ C,in case 2 the outside temperature is -14 ^$\circ$ C.

A)2.1
B)2.2
C)8.4
D)8.8
E)17.3

Question 41

A Carnot engine operates between two reservoirs at 550 K and 250 K.It transfers 300 J to the reservoir at low temperature.The amount of work done is

A)300 J.
B)360 J.
C)545 J.
D)602 J.
E)790 J.

Question 42

A water cooled engine produces 1000 W of power.The engine's thermal efficiency is 36.4% and the rate of water flow is 100.If water enters the engine block at 15 ^$\circ$ C,what is the exit temperature of water?

A)63 ^$\circ$ C
B)85 ^$\circ$ C
C)25 ^$\circ$ C
D)30 ^$\circ$ C
E)46 ^$\circ$ C

Question 43

You have just bought a Carnot refrigerator to keep your food cold.If you intend to run your refrigerator between the cold temperature reservoir at 2.0 ^$\circ$ C (the inside of the box)and the high temperature reservoir at 26 ^$\circ$ C (your kitchen temperature)how much work will be needed to draw 15 J of heat from the cold reservoir?

A)1.2 J
B)1.3 J
C)1.4 J
D)1.5 J

Question 44

A 145-g snowball,initially at 0 ^$\circ$ C,melts in your hands becoming 145 g of water at 20 ^$\circ$ C.What is the change in entropy of the snow/water associated with this event? Remember the latent heat of fusion for water is 334 kJ/kg and the specific heat of liquid water is 4.19 kJ/(kgK).

A)0.18 kJ/K
B)0.22 kJ/K
C)2.0 kJ/K
D)3.4 kJ/K

Question 45

You have just bought a Carnot refrigerator to keep your frozen vegetables frozen.If you intend to run your refrigerator between the cold temperature reservoir at -5 ^$\circ$ C (the inside of the box)and the high temperature reservoir at 26 ^$\circ$ C (your kitchen temperature)how much work will be needed to draw 15 J of heat from the cold reservoir?

A)1.1 J
B)1.2 J
C)1.6 J
D)1.7 J

Question 46

500-g of water at 100 ^$\circ$ C is changed into steam at 100 ^$\circ$ C at constant pressure.The change in entropy of the water is

A)3.03 kJ/K.
B)6.06 kJ/K.
C)8.98 kJ/K.
D)12.5 kJ/K.
E)19.8 kJ/K.

Question 47

A 16-gram lead bullet slams into a concrete wall and melts on impact.If the temperature of the speeding bullet was 25 ^$\circ$ C and if the specific heat of lead is 0.13 kJ/(kgK)and its latent heat of fusion is 23 kJ/kg,what is the change in entropy of the bullet during this process? The melting point of lead is 601K.

A)2.1 J/K
B)0.61 J/K
C)1.5 J/K
D)None are correct.

Question 48

One mole of a monatomic ideal gas at a pressure of 3.0 atm and a volume of 30 L is isothermally expanded to a pressure of 1.0 atm and a volume of 90 L.Afterwards it is compressed at a constant pressure until its volume is 30 L and then it's pressure is increased at a constant volume back to the original volume of 30 L as shown in the PV diagram.What is the efficiency of this heat engine cycle?

A)0.21
B)0.43
C)0.57
D)0.67
E)0.91

Question 49

An 800-kg car traveling at 25 m/s crashes into a wall on a hot day (27 ^$\circ$ C).What is the total change in entropy?

A)39 J/K
B)67 J/K
C)830 J/K
D)1700 J/K
E)9300 J/K

Question 50

What size heat pump with a coefficient of performance of 4.0 is needed for a home that loses heat energy at a rate of 12 kW on the coldest day of the year?

A)3.0 kW
B)4.0 kW
C)6.0 kW
D)12 kW
E)48 kW

Question 51

Your Carnot refrigerator has a coefficient of performance of 5.4.Assume that 15.0 J of heat are removed from the cold refrigerator compartment in each engine cycle.What is the heat expelled into the kitchen for each cycle?

A)2.8 J
B)12.2 J
C)15.0 J
D)15.4 J
E)17.8 J

Question 52

Burning of fuel transfers 5 * 10⁵ W of power into the engine of a 1500-kg vehicle;suppose the maximum speed the vehicle can achieve 5 seconds after starting from rest is 32.6 m/s.Determine the efficiency of the engine.

A)35%
B)25%
C)32%
D)28%
E)20%

Question 53

Burning of fuel transfers power into the engine of a 2000-kg vehicle;suppose the engine has an efficiency of 25% and the maximum speed the vehicle can achieve 5 seconds after starting from rest is 32.6 m/s.Determine the power the fuel transfers to the engine.

A)9.0 * 10⁵ W
B)5.0 * 10⁵ W
C)6.7 * 10⁵ W
D)7.8 * 10⁵ W
E)8.5 * 10⁵ W

Question 54

An ideal Carnot engine takes in 160 kcal of heat at 100 ^$\circ$ C and exhausts some of this at 35 ^$\circ$ C.How much work must have been done by the engine?

A)76.0 kJ
B)116.7 kJ
C)236.6 kJ
D)287.6 kJ
E)307.6 kJ

Question 55

You toss two dice;the total number of ways you can get 12 is

A)1.
B)2.
C)3.
D)4.
E)6.

Question 56

If an engine takes in 600 J of heat and puts out 200 J of heat,what is its efficiency?

A)33%
B)25%
C)75%
D)10%
E)67%

Question 57

A heat pump is operating between two reservoirs at -10 ^$\circ$ C and 50 ^$\circ$ C.The maximum possible coefficient of performance for the heat pump is

A)1.22.
B)2.58.
C)4.79.
D)5.38.
E)9.80.

Question 58

Burning of fuel transfers 4 * 10⁵ W of power into the engine of a 2000-kg vehicle.Suppose the engine has an efficiency of 25% and the vehicle reaches a maximum speed of 32.6 m/s.Assuming the vehicle starts from rest,how long does it take the vehicle to reach this speed?

A)15 seconds
B)5.0 seconds
C)13 seconds
D)9.2 seconds
E)11 seconds

Question 59

A system undergoes a reversible adiabatic process.The entropy change of the system is

A) $\Delta$ S < 0.
B) $\Delta$ S > 0.
C) $\Delta$ S = 0.

Question 60

A bartender mixes 0.1 liter of alcohol which is at room temperature (= 300 K)with 0.3 liter of soda water out of the refrigerator (temperature = 280 K).In this process,

A)the entropy of the water increases and that of the alcohol increases.
B)the entropy of the water decreases and that of the alcohol increases.
C)the entropy of the water increases and that of the alcohol decreases.
D)the entropy of the water decreases and that of the alcohol decreases.
E)Not enough information given,because the specific heat capacities of water and alcohol will decided which entropy will increase,and which will decrease.

Question 61

A heat engine absorbs 130 kcal of heat and exhausts 74 kcal of heat in each cycle.Calculate the efficiency (in %).It is

A)-5.21.
B)0.
C)5.21.
D)22.2.
E)43.1.

Question 62

A car uses 8 liters of gas/hr and does 1.8 kW of useful work.What is the efficiency of the car? (The heat of combustion for 1 liter of gasoline is 3.6 * 10⁶ J.)

A)23%
B)34%
C)37%
D)58%
E)69%

Question 63

Which of the following statements is true?

A)An irreversible process cannot be shown on a p-V diagram because the intermediate states are unknown.
B)The first law of thermodynamics shows that heat added to a system always results in work being done.
C)An adiabatic process is one which involves no work.
D)In an isobaric expansion,the temperature does not change.
E)The second law of thermodynamics does not apply to a closed system.

Question 64

An ideal-gas heat engine operates in a Carnot cycle between temperatures of 266 ^$\circ$ C and 115 ^$\circ$ C.It absorbs 4250 cal per cycle at 266 ^$\circ$ C.What is its efficiency in %?

A)28%
B)36%
C)44%
D)79%
E)100%