Question

Question:A Carnot refrigerator is operated between two heat reservoirs at temperatures of 320 K and 270 K. (a) If in each cycle the refrigerator receives 415 J of heat energy from the reservoir at 270 K, how many joules of heat energy does it deliver to the reservoir at 320 K? (b) If the refrigerator completes 165 cycles each minute, what power input is required to operate it? (c) What is the coefficient of performance of the refrigerator?

Short answer

The heat delivered to reservoir at 320 K is \(492\;{\rm{J}}\).

Step-by-step solution

Identification of given data

The heat received by refrigerator in each cycle is\(Q = 415\;{\rm{J}}\)

The number of hours for daily working of freezer is\(t = 5\;{\rm{h}}\)

The number of cycles per minute for refrigerator is\(n = 165\;{\rm{cycle}}/\min \)

The temperature of first heat reservoir is\({T_1} = 320\;{\rm{K}}\)

The temperature of second heat reservoir is \({T_2} = 270\;{\rm{K}}\)

Conceptual Explanation

The heat delivered to high temperature reservoir is found by equating the thermal efficiency for heat and temperatures.

Determination of heat delivered to first reservoir

The heat delivered to first reservoir is given as:

\({Q_1} = \left( {\frac{{{T_1}}}{{{T_2}}}} \right)Q\)

Substitute all the values in the above equation.

\(\begin{array}{l}{Q_1} = \left( {\frac{{320\;{\rm{K}}}}{{270\;{\rm{K}}}}} \right)\left( {415\;{\rm{J}}} \right)\\{Q_1} \approx 492\;{\rm{J}}\end{array}\)

Therefore, the heat delivered to first reservoir is \(492\;{\rm{J}}\).