A vessel containing 5.0 kg of water at 10°C is put into a refrigerator. The 1/7 HP motor (1 HP = 746 W) runs for 5.0 minutes to cool the liquid to the refrigerator's low temperature, 0°C. What is the κ of the refrigerator?
A) 5.7
B) 4.6
C) 6.5
D) 7.2
E) 3.6

Question

Quizplus · Accepted Answer

First, use the formula Q = mcΔT to find the heat energy required to cool the water from 10°C to 0°C:

Q = (5.0 kg)(4186 J/kg°C)(10°C) = 209,300 J

Next, use the formula P = Q/t to find the power of the refrigerator:

P = (209,300 J)/(5.0 min * 60 s/min) = 698.3 W

Finally, use the formula κ = P/ΔT to find the κ of the refrigerator:

κ = (746 W/1 HP)(1/7 HP)/(10°C) = 6.47 ≈ 6.5

Therefore, the answer is C.

A Vessel Containing 5