A Carnot heat engine receives heat from - Mechanical Engineering

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A Carnot heat engine receives heat from a reservoir at 900°C at a rate of 800 kJ/min and rejects the waste heat to the ambient air at 27°C. The entire work output of the heat engine is used to drive a refrigerator that removes heat from the refrigerated space at 25°C and transfers it to the same ambient air at 27°C. Determine (a) the maximum rate of heat removal from the refrigerated space and (b) the total rate of heat rejection to the ambient air.

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Step 1 of 9

Convert the temperatures in degree Celsius to Kelvin.

The temperature of the reservoir,

The ambient air temperature,

The amount of heat removed for the refrigerator,
Step 2 of 9

Draw the schematic diagram of the heat engine and the reservoir.
Step 3 of 9

(a)

The highest thermal efficiency a heat engine operating between two specified temperature limits can have is the Carnot efficiency.

Calculate the thermal efficiency.

Here, is the sink temperature of the heat engine and is the source temperature of the heat engine.

Substitute for and for .
Step 4 of 9

Calculate the maximum power output of a heat engine by using the following relation.

Here, is the thermal efficiency and is the heat supplied to the heat engine from the reservoir.

Substitute 0.744 for and for .

The power output from the heat engine will be power input to the refrigerant.
Step 5 of 9

Calculate the rate at which the heat rejected from the heat engine.

Here, is the heat supplied to the heat engine from the reservoir, is the heat rejected from the heat engine to the sink, and is the net power output of the heat engine (or) net power input to the refrigerant.

Substitute for and for .
Step 6 of 9

Calculate the coefficient of performance of the refrigerator.

The coefficient of performance of a reversible refrigerator depends upon the temperature limits in the cycle.

Substitute for and for .
Step 7 of 9

Calculate the rate of heat removal from the refrigerated space by using the following relation.

Here, is the coefficient of performance of the refrigerator and is the net power input to the refrigerant.

Substitute 8.375 for and for .

Therefore, the maximum rate of heat removal from the refrigerated space is .
Step 8 of 9

(b)

Calculate the heat rejected from the refrigerator by using the following relation.

Here, is the net power input to the refrigerant and is the heat supplied to the refrigerator.

Substitute for and for .
Step 9 of 9

Calculate the total rate of heat rejection to the ambient air.

Here, is the heat rejection from the heat engine to the ambient air and is the heat rejection from the refrigerator to the ambient air.

Substitute for and for .

Therefore, the total rate of heat rejection to the ambient air is .