# Worksheet: Heat Pumps and Refrigerators

In this worksheet, we will practice calculating the mechanical work required by heat pumps to transfer heat from low to high temperature reservoirs.

Q1:

A refrigerator has a coefficient of performance of 3.0 and it requires an input of J of work per cycle.

How much heat per cycle is removed from the cold reservoir?

How much heat per cycle is discarded to the hot reservoir?

Q2:

A refrigerator discards 80.0 J of heat per cycle and its coefficient of performance is 6.0.

How much heat does the refrigerator remove from its cold reservoir per cycle?

How much work must the refrigerator do per cycle?

Q3:

Calculate the maximum coefficient of performance for a vapor absorption refrigeration system operating with a generator temperature of , an absorber temperature of , and a condenser temperature of . Answer to three-significant-figure precision.

Q4:

A refrigerator with a coefficient of performance of 3.00 is used to produce 5.25 g of ice per second from water at a temperature . What is the minimum input power required by this refrigerator?

Q5:

A Carnot refrigerator operates between temperatures of and . What is its coefficient of performance?

Q6:

Calculate the Carnot coefficient of performance for a refrigeration system operating with a condenser temperature of 300 K and an evaporator temperature of 260 K.

Q7:

In the heat exchanger shown in the accompanying diagram, a fluid enters the pipe at the point 1 at a temperature of . The fluid exits the pipe at the point 3 at a temperature of . Another fluid enters the exchanger’s inner pipe at the point 4. The second fluid enters this pipe at a temperature of and leaves the pipe at the point 2 at a temperature of . What is the logarithmic-mean temperature difference of the fluids?

Q8:

In the heat exchanger shown in the accompanying diagram, a fluid flowing into the exchanger’s inner pipe has a specific heat capacity of . Fluid enters the pipe at the point 1 with a flow rate of 3.00 kg/s and at a temperature of . The fluid exits the pipe at the point 3 at a temperature of . Another fluid with a specific heat capacity of enters the exchanger’s inner pipe at the point 4 with a flow rate of 0.500 kg/s. The second fluid enters this pipe at a temperature of and leaves the pipe at the point 2 at a temperature of . The area of contact between the inner and outer pipes is 2.00 m2. What is the overall heat transfer coefficient in the heat exchanger?

Q9:

In the heat exchanger shown in the accompanying diagram, a fluid flowing into the exchanger’s outer pipe has a specific heat capacity of .Fluid enters the pipe at the point 2 with a flow rate of 3.00 kg/s and at a temperature of .The fluid exits the pipe at the point 4 at a temperature of .Another fluid with a specific heat capacity of enters the exchanger’s inner pipe at the point 1. The second fluid enters this pipe at a temperature of and leaves the pipe at the point 3, at a temperature of . What is the flow rate of the fluid that moves through the inner pipe?

Q10:

During one cycle, a refrigerator removes 450 J from a cold reservoir and rejects 700 J to its hot reservoir.

What is the refrigerator’s coefficient of performance?

How much work per cycle does the refrigerator require to operate?

Q11:

A refrigerator has a coefficient of performance of 2.50. The refrigerator requires 230 J of work per cycle to operate.

How much heat per cycle does the refrigerator extract from the cold reservoir?

How much heat per cycle does the hot reservoir absorb?

Q12:

A Carnot refrigerator operates between the temperatures at its cold reservoir and at its hot reservoir. and vary, causing changes in the work required to cool the cold reservoir by 1.0 J.

Find the work required to cool the cold reservoir by 1.0 J for and .

Find the work required to cool the cold reservoir by 1.0 J for and .

Find the work required to cool the cold reservoir by 1.0 J for and .

Find the work required to cool the cold reservoir by 1.0 J for and .

Q13:

A motor with a power output of 430 W operates a Carnot refrigerator with a cold reservoir temperature of and a hot reservoir temperature of .

What is the rate of cooling of the refrigerator’s interior due to the work done by the refrigerator?

What is the rate of heating of the refrigerator’s exterior due to the work done by the refrigerator?

Q14:

A Carnot heat pump in a house operates between temperatures of and . By how much does the pump heat the house for every 1.0 J of work that it performs?

Q15:

Find the minimum work that a refrigerator must be supplied with if it is to cool a freezer’s interior by 40 J per cycle. The freezer’s interior temperature is and its exterior temperature is .

Q16:

A Carnot engine operates between heat reservoirs at temperatures of 550 K and 350 K. The high-temperature reservoir is heated by 1,400 J per cycle. How much work per cycle does the engine perform?

Q17:

A Carnot refrigerator heats the air around it, which is at a temperature of . Determine how much power the refrigerator requires to freeze 2.0 g of water per second if the water is at an initial temperature of . Use a value of for the specific heat capacity of water and use a value of 334 kJ/kg for the latent heat of fusion of ice.

Q18:

An engineer must design a refrigerator that does 300 J of work per cycle to cool a freezer’s interior at a temperature of by 2,100 J per cycle. What is the maximum air temperature for which this condition can be met?

Q19:

A Carnot cycle is operating between a heat source at a temperature of and a heat sink at a temperature of in order to power a refrigerator that operates between temperatures of and . What power output must the Carnot cycle provide to allow the refrigerator to cool its interior by 13 J/s?

Q20:

In the heat exchanger shown in the accompanying diagram, a fluid flowing into the exchanger’s inner pipe has a specific heat capacity of . Fluid enters the pipe at the point 1 with a flow rate of 3.00 kg/s and at a temperature of . The fluid exits the pipe at the point 3 at a temperature of . Another fluid with a specific heat capacity of enters the exchanger’s inner pipe at the point 4 with a flow rate of 0.500 kg/s. The second fluid enters this pipe at a temperature of and leaves the pipe at the point 2 at a temperature of . The overall heat-transfer coefficient of the heat exchanger is 1,500 W/m2⋅K. What is the area for heat transfer?

Q21:

A refrigerator is kept in a room with temperature of . The refrigerator heats its surroundings at a rate of 1.00 kW. What is the minimum power needed to keep the refrigerator interior at a temperature of ?

Q22:

What is the maximum coefficient of performance of a heat pump, whose temperatures of hot and cold reservoirs are and , respectively?

Q23:

A 300 W heat pump operates between the ground, the temperature of which is , and the interior of a house at . What is the maximum amount of heat per hour that the heat pump can supply to the house? Give your answer to three significant figures.

• A J
• B J
• C J
• D J
• E J