A refrigerator is a heat engine running in reverse. Work that is done on the refrigerator enables it to absorb heat from a low temperature reservoir and release heat to a high temperature reservoir. Consider an ideal refrigerator connected to a 200 K and 400 K reservoir. What is the minimum amount of work (in J) required for this refrigerator to absorb 300 J of energy from the low temperature reservoir

The minimum workdone is    

Explanation:

From the question we are told that

    The temperature range of the reservoir is  

     The energy to absorb is  

The  coefficient of performance for the refrigerator is  mathematically evaluated as

    Substituting value

This coefficient of performance can also be mathematically evaluated as

Where is the minimum workdone

    making  the subject of the formula

So