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4 years ago

8

Two reversible cycles operate between hot and cold reservoirs at temperature TH and TC, respectively. If one is a power cycle an

d the other is a heat pump cycle, what is the relation between the coefficient of performance of the heat pump cycle and the thermal efficiency of the power cycle?

1 answer:

Reika [66]4 years ago

5 0

Answer:

$COP_{HP} = \frac{1}{\eta_{th}}$

Explanation:

The coefficient of performance of the reversible heat pump is:

$COP_{HP} = \frac{T_{H}}{T_{H}-T_{C}}$

$COP_{HP} = \frac{1}{1-\frac{T_{C}}{T_{H}} }$

The thermal efficiency of the reversible power cycle is:

$\eta_{th} = 1 - \frac{T_{C}}{T_{H}}$

After a quick comparison between both expressions, the following relation is found:

$COP_{HP} = \frac{1}{\eta_{th}}$

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3 years ago

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Take the natural log of both sides

$ln 18.182= 0.0000115Q\\2.9004 = 0.0000115Q\\Q = 2.9004/0.0000115\\Q = 252211.49 J/mol\\Q = 252.2 kJ/mol$

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