Cooling of a Canned Drink by a Thermoelectric Refrigerator A thermoelectric refrigerator that resembles a small ice chest is powered by a car battery and has a COP of 0.1. If the refrigerator cools a 0.350-L canned drink from 20 to 4°C in 30 m in, determine the average electric power consumed by

Question

Cooling of a Canned Drink by a Thermoelectric Refrigerator

A thermoelectric refrigerator that resembles a small ice chest is powered by a car battery and has a COP of 0.1. If the refrigerator cools a 0.350-L canned drink from 20 to 4°C in 30 m in, determine the average electric power consumed by the thermoelectric refrigerator.

Accepted Answer

A thermoelectric refrigerator with a specified COP is used to cool canned drinks. The power consumption of the refrigerator is to be determined.

Assumptions Heat transfer through the walls of the refrigerator is negligible during operation.

Properties The properties of canned drinks are the same as those of water at room temperature, [latex] ho=1 \mathrm{~kg} / \mathrm{L}[/latex] and [latex]c=4.18 \mathrm{~kJ} / \mathrm{kg} \cdot{ }^{\circ} \mathrm{C}[/latex] (Table A-3).

Analysis The cooling rate of the refrigerator is simply the rate of decrease of the energy of the canned drinks,

[latex]m= ho V=(1 \mathrm{~kg} / \mathrm{L})(0.350 \mathrm{~L})=0.350 \mathrm{~kg} [/latex]

[latex]Q_{ ext {cooling }}=m c \Delta T=(0.350 \mathrm{~kg})\left(4.18 \mathrm{~kJ} / \mathrm{kg} \cdot{ }^{\circ} \mathrm{C} ight)(20-4){ }^{\circ} \mathrm{C}=23.4 \mathrm{~kJ} [/latex]

[latex]\dot{Q}_{ ext {cooling }}=\frac{Q_{ ext {cooling }}}{\Delta t}=\frac{23.4 \mathrm{~kJ}}{30 imes 60 \mathrm{~s}}=0.0130 \mathrm{~kW}=13 \mathrm{~W}[/latex]

Then the average power consumed by the refrigerator becomes

[latex]\dot{W}_{ ext {in }}=\frac{\dot{Q}_{ ext {cooling }}}{\mathrm{COP}_{\mathrm{R}}}=\frac{13 \mathrm{~W}}{0.10}=130 \mathrm{~W}[/latex]

Discussion In reality, the power consumption will be larger because of the heat gain through the walls of the refrigerator.

Question 11.7: Cooling of a Canned Drink by a Thermoelectric Refrigerator A...

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