Question 1

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

Accepted Answer

The efficiency of a Carnot air conditioner is given by the formula: COP = T_c / (T_h - T_c), where T_c and T_h are the absolute temperatures (in Kelvin) of the cold and hot reservoirs, respectively. Converting the temperatures to Kelvin, T_c = 293 K and T_h = 312 K. The COP is 293 / (312 - 293) = 15.42. The work done (energy needed) is Q_c / COP = 2000 J / 15.42 ≈ 130 J.

Question 2

A Carnot engine operating between a reservoir of liquid mercury at its melting point (233 K)and a colder reservoir extracts  of heat from the mercury and does  of work during each cycle.What is the temperature of the colder reservoir?

Accepted Answer

The answer of A Carnot engine operating between a reservoir...

Question 3

A certain Carnot heat pump transfers energy from the outside of a house,where the temperature is -15°C,to the inside of a room where the temperature is 21°C.If this heat pump runs off of electricity,what is the minimum rate at which it uses electrical energy to deliver 150 W to the inside room?

Accepted Answer

The answer of A certain Carnot heat pump transfers energy...

Question 4

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

Accepted Answer

The answer of A Carnot engine operates between a high...

Question 5

An ideal Carnot engine operates between reservoirs having temperatures of 125°C and
-20°C.Each cycle the heat expelled by this engine is used to melt 30.0 g of ice at 0.00°C.The heat of fusion of water is  and the heat of vaporization of water is  .
(a)How much work does this engine do each cycle?
(b)How much heat per cycle does this engine absorb at the hot reservoir?

Accepted Answer

The answer of An ideal Carnot engine operates between reservoirs...

Question 6

What is the maximum theoretical efficiency possible for a heat 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 atmosphere for both reservoirs.

Accepted Answer

The maximum theoretical efficiency of a heat engine is given by the Carnot efficiency, which is calculated using the temperatures of the hot and cold reservoirs (Th and Tc, respectively) in Kelvin. The temperature at which ice and water coexist (the melting point of ice) is 0°C or 273K, and the temperature at which water and steam coexist (the boiling point of water) is 100°C or 373K under 1.0 atmosphere pressure. The Carnot efficiency is given by 1 - (Tc/Th), so the efficiency is 1 - (273/373) = 0.268, or 26.8%, which rounds to approximately 27%.

Question 7

A Carnot refrigerator takes heat from water at 0°C and rejects heat to a room at 12°C.Suppose that 92.0 grams of water at 0°C are converted to ice at 0°C by the refrigerator.Calculate the mechanical energy that must be supplied to the refrigerator.The heat of fusion of water is 3.34 × 10⁵ J/kg.

Accepted Answer

The answer of A Carnot refrigerator takes heat from water...

Question 8

A Carnot engine operates between reservoirs at 550K and 300K,discarding  of heat in each cycle.
(a)What is the engine's efficiency?
(b)How much heat is supplied to the engine by the hot reservoir in each cycle?

Accepted Answer

The answer of A Carnot engine operates between reservoirs at...

Question 9

A perfect Carnot engine operates between the temperatures of 300K and 700K,drawing 60 kJ of heat from the 700K reservoir in each cycle.How much heat is dumped into the 300K reservoir in each cycle?

Accepted Answer

The answer of A perfect Carnot engine operates between the...

Question 10

A coal-fired plant generates 600 MW of electric power.The plant uses  of coal each day.The heat produced by the combustion of coal is  .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)What is the maximum efficiency that this plant could possibly have using the same temperature extremes that it presently uses?
(c)How much thermal energy is exhausted each day by this plant?

Accepted Answer

The answer of A coal-fired plant generates 600 MW of...

Question 11

An ideal reversible refrigerator keeps its inside compartment at 9.0°C.What is the high temperature,T_h,needed to give this refrigerator a coefficient of performance of 3.7?

Accepted Answer

The coefficient of performance of a refrigerator is given by the ratio of the heat removed from the cold reservoir to the work done. In this case, the coefficient of performance is 3.7, so the heat removed from the cold reservoir is 3.7 times the work done. The heat removed from the cold reservoir is equal to the heat absorbed by the refrigerant, which is equal to the difference in temperature between the high and low temperatures multiplied by the specific heat of the refrigerant. The work done is equal to the difference in temperature between the high and low temperatures multiplied by the Carnot efficiency. Therefore, the coefficient of performance is equal to the ratio of the specific heat of the refrigerant to the Carnot efficiency. In this case, the specific heat of the refrigerant is 1, so the Carnot efficiency is 1/3.7 = 0.27. The Carnot efficiency is equal to 1 - T_c/T_h, where T_c is the low temperature and T_h is the high temperature. Therefore, T_h = T_c/(1 - Carnot efficiency) = 9°C/(1 - 0.27) = 85°C.

Question 12

A Carnot refrigerator has a coefficient of performance of 2.5.The refrigerator consumes 50 W of power.How much heat is removed from the interior of the refrigerator in 1 hour?

Accepted Answer

The coefficient of performance (COP) for a refrigerator is defined as the ratio of the heat removed from the refrigerator (Q_c) to the work input (W). Given COP = 2.5 and W = 50 W, we can calculate Q_c as follows: COP = Q_c / W, so Q_c = COP * W = 2.5 * 50 W = 125 W. To find the heat removed in 1 hour, convert power (in watts) to energy (in joules) using the conversion 1 W = 1 J/s. Thus, 125 J/s * 3600 s = 450,000 J or 450 kJ.

Question 13

One of the most efficient engines built so far has the following characteristics: combustion chamber temperature = 1900°C exhaust temperature = 430°C 7.0 × 10⁹ cal of fuel produces 1.4 × 10¹⁰ J of work in one hour,where (a)What is the actual efficiency of this engine? (b)What is the Carnot efficiency of the engine? (c)What is the power output of this engine?

Accepted Answer

The answer of One of the most efficient engines built...

Question 14

A Carnot engine is operated as a heat pump to heat a room in the winter.The heat pump delivers heat to the room at the rate of  per second and maintains the room at a temperature of  when the outside temperature is  The power requirement for the heat pump under these operating conditions is closest to

Accepted Answer

The answer of A Carnot engine is operated as a...

Question 15

The compressor in a certain Carnot refrigerator performs 480 J of work to remove 150 J of heat from the interior of the refrigerator.How much heat must the coils behind the refrigerator discharge into the kitchen?

Accepted Answer

The Carnot refrigerator operates on the principle of conservation of energy. The work done by the compressor (480 J) is used to remove heat from the interior (150 J) and the rest is discharged as heat into the surroundings. Therefore, the heat discharged is the sum of the work done and the heat removed from the interior: 480 J + 150 J = 630 J.

Question 16

An air conditioner with a coefficient of performance of 3.5 uses 30 kW of power.How much power is it discharging to the outdoors?

Accepted Answer

The answer of An air conditioner with a coefficient of...

Question 17

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

Accepted Answer

The answer of A refrigerator has a coefficient of performance...

Question 18

You want to design an ideal Carnot heat engine that wastes only 35.0% of the heat that goes into it.The lowest cold-reservoir temperature available to you is +15.0°C.If  of work is done per cycle,the heat input per cycle is closest to

Accepted Answer

The answer of You want to design an ideal Carnot...

Question 19

A Carnot cycle engine operates between a low temperature reservoir at 20°C and a high temperature reservoir at 800°C.If the engine is required to output  of work per cycle,how much heat must the high temperature reservoir transfer to the engine during each cycle?

Accepted Answer

The answer of A Carnot cycle engine operates between a...

Question 20

The temperature inside a Carnot refrigerator placed in a kitchen at 22.0°C is 2.0°C.The heat extracted from the refrigerator is 89 MJ/h.What power is needed to operate this refrigerator?

Accepted Answer

The coefficient of performance (COP) of Carnot refrigerator is given by:
COP = (absolute temperature of low temperature reservoir)/(absolute temperature of high temperature reservoir - absolute temperature of low temperature reservoir)

Here, the high temperature reservoir is the temperature of the kitchen (22.0°C = 295.2 K) and the low temperature reservoir is the temperature inside the refrigerator (2.0°C = 275.2 K).

COP = 275.2 K / (295.2 K - 275.2 K) = 13.76

The energy input to the refrigerator is Qh/COP, where Qh is the heat extracted from the refrigerator.

Power = Qh/COP = (89 MJ/h)/(13.76) = 6.47 kW

Therefore, the power needed to operate the refrigerator is 6.47 kW, which is closest to option B (1.8 kW).

Quiz 20: The Second Law of Thermodynamics

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

A Carnot engine operating between a reservoir of liquid mercury at its melting point (233 K) and a colder reservoir extracts of heat from the mercury and does of work during each cycle.What is the temperature of the colder reservoir?

A certain Carnot heat pump transfers energy from the outside of a house,where the temperature is -15°C,to the inside of a room where the temperature is 21°C.If this heat pump runs off of electricity,what is the minimum rate at which it uses electrical energy to deliver 150 W to the inside room?

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

What is the maximum theoretical efficiency possible for a heat 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 atmosphere for both reservoirs.

A Carnot engine operates between reservoirs at 550K and 300K,discarding of heat in each cycle. (a)What is the engine's efficiency? (b)How much heat is supplied to the engine by the hot reservoir in each cycle?

A perfect Carnot engine operates between the temperatures of 300K and 700K,drawing 60 kJ of heat from the 700K reservoir in each cycle.How much heat is dumped into the 300K reservoir in each cycle?

An ideal reversible refrigerator keeps its inside compartment at 9.0°C.What is the high temperature,T_h,needed to give this refrigerator a coefficient of performance of 3.7?

A Carnot refrigerator has a coefficient of performance of 2.5.The refrigerator consumes 50 W of power.How much heat is removed from the interior of the refrigerator in 1 hour?

A Carnot engine is operated as a heat pump to heat a room in the winter.The heat pump delivers heat to the room at the rate of per second and maintains the room at a temperature of when the outside temperature is The power requirement for the heat pump under these operating conditions is closest to

The compressor in a certain Carnot refrigerator performs 480 J of work to remove 150 J of heat from the interior of the refrigerator.How much heat must the coils behind the refrigerator discharge into the kitchen?

An air conditioner with a coefficient of performance of 3.5 uses 30 kW of power.How much power is it discharging to the outdoors?

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

You want to design an ideal Carnot heat engine that wastes only 35.0% of the heat that goes into it.The lowest cold-reservoir temperature available to you is +15.0°C.If of work is done per cycle,the heat input per cycle is closest to

A Carnot cycle engine operates between a low temperature reservoir at 20°C and a high temperature reservoir at 800°C.If the engine is required to output of work per cycle,how much heat must the high temperature reservoir transfer to the engine during each cycle?

The temperature inside a Carnot refrigerator placed in a kitchen at 22.0°C is 2.0°C.The heat extracted from the refrigerator is 89 MJ/h.What power is needed to operate this refrigerator?

Quiz 20: The Second Law of Thermodynamics

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

A Carnot engine operating between a reservoir of liquid mercury at its melting point (233 K) and a colder reservoir extracts of heat from the mercury and does of work during each cycle.What is the temperature of the colder reservoir?

A certain Carnot heat pump transfers energy from the outside of a house,where the temperature is -15°C,to the inside of a room where the temperature is 21°C.If this heat pump runs off of electricity,what is the minimum rate at which it uses electrical energy to deliver 150 W to the inside room?

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

What is the maximum theoretical efficiency possible for a heat 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 atmosphere for both reservoirs.

A Carnot engine operates between reservoirs at 550K and 300K,discarding of heat in each cycle. (a)What is the engine's efficiency? (b)How much heat is supplied to the engine by the hot reservoir in each cycle?

A perfect Carnot engine operates between the temperatures of 300K and 700K,drawing 60 kJ of heat from the 700K reservoir in each cycle.How much heat is dumped into the 300K reservoir in each cycle?

An ideal reversible refrigerator keeps its inside compartment at 9.0°C.What is the high temperature,Th,needed to give this refrigerator a coefficient of performance of 3.7?

A Carnot refrigerator has a coefficient of performance of 2.5.The refrigerator consumes 50 W of power.How much heat is removed from the interior of the refrigerator in 1 hour?

A Carnot engine is operated as a heat pump to heat a room in the winter.The heat pump delivers heat to the room at the rate of per second and maintains the room at a temperature of when the outside temperature is The power requirement for the heat pump under these operating conditions is closest to

The compressor in a certain Carnot refrigerator performs 480 J of work to remove 150 J of heat from the interior of the refrigerator.How much heat must the coils behind the refrigerator discharge into the kitchen?

An air conditioner with a coefficient of performance of 3.5 uses 30 kW of power.How much power is it discharging to the outdoors?

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

You want to design an ideal Carnot heat engine that wastes only 35.0% of the heat that goes into it.The lowest cold-reservoir temperature available to you is +15.0°C.If of work is done per cycle,the heat input per cycle is closest to

A Carnot cycle engine operates between a low temperature reservoir at 20°C and a high temperature reservoir at 800°C.If the engine is required to output of work per cycle,how much heat must the high temperature reservoir transfer to the engine during each cycle?

The temperature inside a Carnot refrigerator placed in a kitchen at 22.0°C is 2.0°C.The heat extracted from the refrigerator is 89 MJ/h.What power is needed to operate this refrigerator?

An ideal reversible refrigerator keeps its inside compartment at 9.0°C.What is the high temperature,T_h,needed to give this refrigerator a coefficient of performance of 3.7?