Derive an expression for co-efficient of performance of refrigerator.

1.	Derive an expression for co-efficient of performance of refrigerator.
Answer» <html><body><p></p>Solution :Coefficient of performance (COP)`(beta)`: COP is a <a href="https://interviewquestions.tuteehub.com/tag/measure-1091857" style="font-weight:bold;" target="_blank" title="Click to know more about MEASURE">MEASURE</a> of the efficiency of a <a href="https://interviewquestions.tuteehub.com/tag/refrigerator-1181966" style="font-weight:bold;" target="_blank" title="Click to know more about REFRIGERATOR">REFRIGERATOR</a>. It is defined as the ratio of heat extracted from the cold <a href="https://interviewquestions.tuteehub.com/tag/body-900196" style="font-weight:bold;" target="_blank" title="Click to know more about BODY">BODY</a> (sink) to the <a href="https://interviewquestions.tuteehub.com/tag/external-981194" style="font-weight:bold;" target="_blank" title="Click to know more about EXTERNAL">EXTERNAL</a> work <a href="https://interviewquestions.tuteehub.com/tag/done-2591742" style="font-weight:bold;" target="_blank" title="Click to know more about DONE">DONE</a> by the compressor W. <br/> COP `= beta = (Q_(L))/W`...(1) <br/> From the equation `Q_(L)+W=Q_(H)` <br/> `beta = (Q_(L))/(Q_(H) - Q_(L))` <br/> `beta = (1)/((Q_(H))/(Q_(L)) - 1)`...(2) <br/> But we know that `(Q_(H))/(Q_(L)) = (T_(H))/(T_(L))` <br/> Substituting this equation into equation (1) we get `beta = (1)/((T_(H))/(T_(L)) - 1) = (T_(L))/(T_(H) - T_(L))`</body></html>

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