Reversed Heat Engines

01Reversed Heat Engines

Reversed heat engines

This section covers how a reversed heat engine uses work to transfer thermal energy from a cold space to a hotter space.

Reversing the thermal transfer

A reversed heat engine transfers thermal energy from a cold space at temperature $T_C$ to a hotter space at temperature $T_H$ .

Work must be supplied because spontaneous thermal transfer occurs in the opposite direction: from higher temperature to lower temperature.

The device removes energy $Q_C$ from the cold region. Work $W$ is supplied to the device, which then transfers energy $Q_H$ into the hotter region.

Conservation of energy gives

Q_H=Q_C+W

Quantity	Meaning
$Q_C$	Energy extracted from the cold space.
$W$	Work supplied to the device.
$Q_H$	Energy delivered to the hot space.

Since the work input also contributes to the energy delivered to the hot space, $Q_H$ is greater than $Q_C$ .

Reversed heat engines are used in refrigerators, air-conditioning systems and heat pumps.

Exam Tip: In a reversed heat-engine diagram, $Q_C$ must point from the cold space into the device, $W$ must point into the device, and $Q_H$ must point from the device into the hot space.

02Reversed Heat Engines

Refrigerators & heat pumps

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Same transfers, different purpose

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Refrigerator

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Heat pump

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03Reversed Heat Engines

Refrigerator COP

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Useful cooling per unit work

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COP_{\mathrm{ref}}=\frac{Q_C}{W}

Ppawd

Q_H=Q_C+W,

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COP_{\mathrm{ref}}=\frac{Q_C}{Q_H-Q_C}

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04Reversed Heat Engines

Heat pump COP

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Useful heating per unit work

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COP_{\mathrm{hp}}=\frac{Q_H}{W}

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COP_{\mathrm{hp}}=\frac{Q_H}{Q_H-Q_C}

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COP_{\mathrm{hp}}=COP_{\mathrm{ref}}+1

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05Reversed Heat Engines

Maximum COP

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Temperature-based limits

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Device	Maximum theoretical COP
Dmcqrhmitpyk	$COP_{\mathrm{ref,max}}=\frac{T_C}{T_H-T_C}$
Rdsp mfln	$COP_{\mathrm{hp,max}}=\frac{T_H}{T_H-T_C}$

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COP_{\mathrm{hp,max}}=COP_{\mathrm{ref,max}}+1

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