GATE Mechanical Engineering (ME) 2019 Shift 2 Solved Paper

Question : 57 of 65

Marks: +1, -0

The figure shows a heat engine (HE) working between two reservoirs. The amount of heat

( {Q}_{2})

rejected by the heat engine is drawn by a heat pump (HP). The heat pump receives the entire work output

( {W})

of the heat engine. If temperatures.

{T}_{1}> {T}_{3}> {T}_{2}

, then the relation between the efficiency (

η

) of the heat engine and the coefficient of performance (COP) of the heat pump is

T_{2}

Solution:

For heat engine,

η=\;{W}/{Q_{1}}

For Heat engine,

C O P=\;{Q_{3}}/{w}

Energy balance for Heat engine gives

Q_{2}=Q_{1}-W

And energy balance for Heat pump gives

Q_{3}=Q_{2}+W=Q_{1}-W+W=Q_{1}

Hence,

C O P=\;{Q_{1}}/{W}=\;{1}/{η}=η^{-1}

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