A cold body is to be maintained at low temperature T2 when the temperature of surrounding is T3. A source is available at high temperature T1. Obtain the expression for minimum theoretical ratio of heat supplied from source to heat absorbed from cold body.

Question

A cold body is to be maintained at low temperature [latex] extbf{T}_{2}[/latex] when the temperature of surrounding is [latex] extbf{T}_{3}[/latex]. A source is available at high temperature [latex] extbf{T}_{1}[/latex]. Obtain the expression for minimum theoretical ratio of heat supplied from source to heat absorbed from cold body.

Accepted Answer

[latex] ext{Let us consider a refrigerator for maintaining cold body and also a reversible heat engine for driving refrigerator to}\ ext{ operate together, Fig 4.35.}\ ext{To obtain; }\frac{Q_{1}}{Q_{3}}\\begin{aligned} ext{For heat engine, }\frac{W}{Q_{1}}&= \frac{T_{1} - T_{3}}{T_{1}}\ ext{For refrigerator, }\frac{Q_{3}}{W}&= \frac{T_{2}}{T_{3} - T_{2}}\ ext{Combining the above two:} &\\frac{Q_{1}}{Q_{3}}&= \frac{T_{1} imes (T_{3} - T_{2})}{T_{2} imes (T_{1} - T_{3})}\end{aligned}\ ext{Ratio of heat supplied from source to heat absorbed from cold body =}\frac{T_{1} . (T_{3} - T_{2})}{T_{2} . (T_{1} - T_{3})}[/latex]

Question 4.17: A cold body is to be maintained at low temperature T2 when t...

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