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Internal Energy

A heat pump w...

Question

A heat pump with a COP of 2.8 is used to heat an air-tight house. When running, the heat pump consumes 5 kW of power. The temperature in the house is 7°C when the heat pump is turned on. Assuming the entire mass within the house (air, furniture, etc) is equivalent to 1500kg of air. How long will it take for the heat pump to raise the temperature of the house to 22°C?

A

19.2 min

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B

17.1 min

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C

14.2 min

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D

24.6 min

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Solution

The correct option is A 19.2 min
$C O P = 2.8 = \frac{H e a t s u p p l i e d}{W o r k i n p u t}$
Heat supplied = 2.8×5 = 14kW
Let in 't' time, temperature of house becomes 22°C. Applying first law of thermodynamics to the air within the house
Q - W = $Δ$ U
$0 - [- 14 \times t] = m \times C_{v} \times d T$

$14 \times t = 1500 \times 0.717 \times 15$
t = 19.2min

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