Question 1

The "hot shot" heat 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 heat at a rate of 60 kW, at what rate does it exhaust heat?
A) 41 kW
B) 36 kW
C) 60 kW
D) 57 kW

Accepted Answer

The efficiency of an ideal Carnot engine is given by $ \eta = 1 - \frac{T_c}{T_h} $, where $ T_c $ and $ T_h $ are the cold and hot reservoir temperatures in Kelvin, respectively. Converting the given temperatures to Kelvin gives $ T_c = 40 + 273 = 313 $ K and $ T_h = 380 + 273 = 653 $ K. Thus, the efficiency of the ideal Carnot engine is $ \eta = 1 - \frac{313}{653} $.The "hot shot" engine's efficiency is 60% of this, so its efficiency is $ 0.6 \times \left(1 - \frac{313}{653}\right) $.The rate at which work is done (or power output) by the engine is the product of its efficiency and the rate at which it absorbs heat, which is $ 0.6 \times \left(1 - \frac{313}{653}\right) \times 60 $ kW.The rate at which it exhausts heat is the difference between the rate at which it absorbs heat and the rate at which it does work. Thus, the rate at which it exhausts heat is $ 60 $ kW - $ 0.6 \times \left(1 - \frac{313}{653}\right) \times 60 $ kW. Calculating this gives approximately 41 kW.

Question 2

An ideal Carnot engine is operated as an air conditioner to cool a house in the summer. The air conditioner removes 14 kJ of heat per second from the house, and maintains the inside
Temperature at 293 K, while the outside temperature is 369 K. The power required to run the air
Conditioner under these operating conditions is closest to
A) 5800 W.
B) 4400 W.
C) 5100 W.
D) 3600 W.
E) 6600 W.

Accepted Answer

The answer of An ideal Carnot engine is operated as...

Question 3

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

Accepted Answer

The efficiency of a heat engine is given by the equation:```efficiency = 1 - (T_c / T_h)```where:* T_c is the temperature of the cold reservoir* T_h is the temperature of the hot reservoirIf the efficiency is 35.0% and the temperature of the hot reservoir is 700 K, then the temperature of the cold reservoir can be found by solving the equation for T_c:```0.35 = 1 - (T_c / 700 K)T_c = 700 K - 0.35 * 700 KT_c = 455 K```Therefore, the temperature of the cold reservoir is 455 K.

Question 4

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

Accepted Answer

The answer of An ideal Carnot engine has an efficiency...

Question 5

During each cycle, the compressor in a certain ideal Carnot refrigerator performs 480 J of work to remove 150 J of heat from the interior of the refrigerator. How much heat do the coils behind the
Refrigerator discharge into the kitchen each cycle?
A) 110 J
B) 150 J
C) 480 J
D) 630 J
E) 330 J

Accepted Answer

The heat discharged into the kitchen each cycle is the sum of the work done by the compressor and the heat removed from the refrigerator's interior. Therefore, it is 480 J (work done) + 150 J (heat removed) = 630 J.

Question 6

An external heat source supplies heat to a system at a rate of 187 W as the system does work at a rate of 131 W. At what rate is the internal (thermal) energy of the system changing?
A) -320 W
B) -56 W
C) 190 W
D) 320 W
E) 56 W

Accepted Answer

The rate of change of internal energy in a system is given by the difference between the heat supplied to the system and the work done by the system. Therefore, the rate of change of internal energy is 187 W - 131 W = 56 W.

Question 7

An ideal Carnot heat engine has an efficiency of 0.600. If it operates between a deep lake with a constant temperature of 294.0 K and a hot reservoir, what is the temperature of the hot reservoir?
A) 735 K
B) 470 K
C) 784 K
D) 490 K

Accepted Answer

The efficiency of a Carnot heat engine is given by:$$e = 1 - \frac{T_c}{T_h}$$where $T_c$ is the temperature of the cold reservoir and $T_h$ is the temperature of the hot reservoir.We are given that $e = 0.600$ and $T_c = 294.0 K$. Solving for $T_h$, we get:$$T_h = \frac{T_c}{1 - e} = \frac{294.0 K}{1 - 0.600} = 735 K$$Therefore, the temperature of the hot reservoir is 735 K.

Question 8

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 heat from the interior of
The house?
A) 340 J
B) 780 J
C) 105 J
D) 130 J
E) 520 J

Accepted Answer

The efficiency of a Carnot air conditioner is determined by the temperatures of the hot and cold reservoirs. The formula for the coefficient of performance (COP) of a Carnot refrigerator is COP = Tc / (Th - Tc), where Tc and Th are the absolute temperatures (in Kelvin) of the cold and hot reservoirs, respectively. Converting the given temperatures to Kelvin: Tc = 20°C + 273 = 293 K, Th = 39°C + 273 = 312 K. The COP is 293 / (312 - 293) = 293 / 19 = 15.42. The work done (energy used) is the heat removed divided by the COP: 2000 J / 15.42 ≈ 130 J.

Question 9

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 heat from the interior compartment?
A) 1050 J
B) 480 J
C) 250 J
D) 120 J
E) 60 J

Accepted Answer

The coefficient of performance (COP) for a refrigerator is given by COP = Qc/W, where Qc is the heat removed from the interior and W is the work done. Rearranging gives W = Qc/COP. Substituting the given values, W = 250 J / 4.2 = 59.52 J, which rounds to 60 J.

Question 10

An ideal Carnot engine extracts 529 J of heat from a high-temperature reservoir during each cycle, and rejects 225 J of heat to a low-temperature reservoir during the same cycle. What is the
Efficiency of the engine?
A) 0.7
B) 1.35
C) 2.35
D) 0.57

Accepted Answer

The efficiency of a Carnot engine is given by the formula: Efficiency = 1 - (Qc/Qh), where Qc is the heat rejected and Qh is the heat absorbed. Here, Efficiency = 1 - (225/529) = 0.57.

Question 11

An ideal reversible heat 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 heat pump?
A) 0.533
B) 10.4
C) 0.644
D) 0.0962
E) 9.44

Accepted Answer

The coefficient of performance (COP) of a heat pump is given by COP = Qc / W, where Qc is the heat delivered to the warm space and W is the work input. For an ideal reversible heat pump, the COP can also be calculated using the temperatures of the heat source and sink: COP = Tc / (Th - Tc), where Tc is the absolute temperature of the heat source (in Kelvin) and Th is the absolute temperature of the heat sink (in Kelvin). Converting the given temperatures to Kelvin: -10.0°C = 263.15 K and 18.0°C = 291.15 K. Thus, COP = 291.15 / (291.15 - 263.15) = 291.15 / 28 = 10.4.

Question 12

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

Accepted Answer

The maximum possible efficiency of a heat engine is given by the Carnot efficiency, which is $1 - \frac{T_c}{T_h}$, where $T_c$ is the temperature of the cold reservoir and $T_h$ is the temperature of the hot reservoir. Given that the efficiency is 25% (or 0.25) and $T_c = 300$ K, we can set up the equation $0.25 = 1 - \frac{300}{T_h}$. Solving for $T_h$ gives $T_h = 400$ K.

Question 13

The gas in a perfectly insulated but flexible container does work at a rate of 13 W. At what rate is the internal (thermal) energy of the gas changing?
A) 13 W
B) 0 W
C) 6.5 W
D) -13 W

Accepted Answer

In an insulated system, no heat is exchanged with the surroundings. According to the first law of thermodynamics, the change in internal energy is equal to the heat added to the system minus the work done by the system. Since no heat is added, the change in internal energy is equal to the negative of the work done, which is -13 W.

Question 14

A fluid in an insulated, flexible bottle is heated by a high resistance wire and expands. If 9.0 kJ of heat is applied to the system and it does 5.0 kJ of work, how much does the internal (thermal)
Energy of the fluid change?
A) 14 kJ
B) -4.0 kJ
C) 4.0 kJ
D) 45 kJ

Accepted Answer

The change in internal energy (ΔU) of the system can be calculated using the first law of thermodynamics, which is ΔU = Q - W, where Q is the heat added to the system and W is the work done by the system. Here, Q = 9.0 kJ (heat added) and W = 5.0 kJ (work done by the system). Thus, ΔU = 9.0 kJ - 5.0 kJ = 4.0 kJ.

Question 15

A nuclear power plant has an actual efficiency of 33%. If 0.19 MW of energy are released from fission, how much electric power does the power plant produce?
A) 25 MW
B) 0.25 MW
C) 6.3 MW
D) 0.063 MW

Accepted Answer

The electric power produced is 33% of 0.19 MW, which is 0.063 MW.

Question 16

A Carnot air conditioner has a coefficient of performance of 17.0 and removes 72.0 MJ of heat from the interior of a house every hour. How much power does it consume?
A) 3.14 MW
B) 1320 W
C) 520 kW
D) 1180 W
E) 1.25 MW

Accepted Answer

The power consumed by the air conditioner can be calculated using the formula: Power = Heat removed / COP. Here, Heat removed = 72.0 MJ/hour = 72,000,000 J/hour = 20,000 J/s (since 1 hour = 3600 seconds), and COP = 17.0. Therefore, Power = 20,000 J/s / 17.0 = 1176.47 W, which is approximately 1180 W.

Question 17

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
Heat pump. What is its thermal efficiency when operated as a heat engine doing work?
A) 80%
B) 20%
C) 25%
D) 10%
E) 45%

Accepted Answer

The COP of a refrigerator is related to the efficiency of a heat engine by the relation COP = 1/(1 - η), where η is the efficiency. Given COP = 4 for the refrigerator, η = 1 - 1/4 = 0.75. However, for a heat engine, the efficiency is η = 1 - 1/COP_heat_pump. Given COP_heat_pump = 5, η = 1 - 1/5 = 0.20 or 20%.

Question 18

A fixed amount of an ideal monatomic gas is maintained at constant volume as it is cooled by 50 K. This feat is accomplished by removing 400 J of energy from the gas. How much work is done by
The gas during this process?
A) 400 J
B) 200 J
C) -400 J
D) -200 J
E) 0 J

Accepted Answer

When a gas is maintained at constant volume and cooled, the work done by the gas is zero because work (W) is defined as W = PΔV, where P is pressure and ΔV is the change in volume. Since the volume does not change (ΔV = 0), no work is done.

Question 19

During each cycle of operation, a refrigerator absorbs 230 J of heat from the freezer and expels 356 J of heat to the room. How much work input is required in each cycle?
A) 586 J
B) 126 J
C) 712 J
D) 460 J

Accepted Answer

The work input required for each cycle can be calculated using the first law of thermodynamics, which in the context of a refrigerator is often simplified to the equation: Work input = Heat expelled - Heat absorbed. Therefore, the work input is 356 J - 230 J = 126 J.

Question 20

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) 210 kW
C) 105 kW
D) 135 kW
E) 75.0 kW

Accepted Answer

The coefficient of performance (COP) is defined as the ratio of the heat removed from the indoors (Qc) to the work input (W). COP = Qc/W. Given COP = 3.50 and W = 30.0 kW, we find Qc = COP * W = 3.50 * 30.0 kW = 105 kW. The total power discharged to the outdoors (Qh) is the sum of the power used and the heat removed: Qh = Qc + W = 105 kW + 30.0 kW = 135 kW.

Quiz 2: Describing Motion: Kinematics in One Dimension

The "hot shot" heat 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 heat at a rate of 60 kW, at what rate does it exhaust heat?

A heat 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?

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?

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

An external heat source supplies heat to a system at a rate of 187 W as the system does work at a rate of 131 W. At what rate is the internal (thermal) energy of the system changing?

An ideal Carnot heat engine has an efficiency of 0.600. If it operates between a deep lake with a constant temperature of 294.0 K and a hot reservoir, what is the temperature of the hot reservoir?

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 heat from the interior of The house?

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 heat from the interior compartment?

An ideal Carnot engine extracts 529 J of heat from a high-temperature reservoir during each cycle, and rejects 225 J of heat to a low-temperature reservoir during the same cycle. What is the Efficiency of the engine?

An ideal reversible heat 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 heat pump?

A heat 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?

The gas in a perfectly insulated but flexible container does work at a rate of 13 W. At what rate is the internal (thermal) energy of the gas changing?

A fluid in an insulated, flexible bottle is heated by a high resistance wire and expands. If 9.0 kJ of heat is applied to the system and it does 5.0 kJ of work, how much does the internal (thermal) Energy of the fluid change?

A nuclear power plant has an actual efficiency of 33%. If 0.19 MW of energy are released from fission, how much electric power does the power plant produce?

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

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 Heat pump. What is its thermal efficiency when operated as a heat engine doing work?

A fixed amount of an ideal monatomic gas is maintained at constant volume as it is cooled by 50 K. This feat is accomplished by removing 400 J of energy from the gas. How much work is done by The gas during this process?

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

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?