We want to determine how much the room temperature increases when a kg of ice fr
ID: 1586335 • Letter: W
Question
We want to determine how much the room temperature increases when a kg of ice freezes. Suppose you have a freezer that needs 1 J of energy for every 3 J of heat it removes.
How much thermal energy must be removed from 1 kg of water at room temperature?
How much electrical energy is used to freeze the ice?
What is the total energy, including waste heat, that is dumped into the kitchen?
If the kitchen contains 40 kg of air, how much will the temperature rise?
What is the efficiency of the freezer? (The latent heat of water for freezing is 80 cal/gm°C, and the specific heat of air is about 0.2 cal/gm°C. We know you could look it up; we thought we'd save you the time.)
Explanation / Answer
Here ,
heat removed from ice , Qc = 3 J
work done, W = 1 J
for the 1 Kg of water at room temperature
thermal energy removed = 1 * (4186 * (25) + 334 *10^3)
thermal energy removed = 4.39 *10^5 J
the thermal energy removed from 1 Kg ice is 4.39 *10^5 J
electrical energy used = thermal energy removed/3
electrical energy used = (4.39 *10^5 J)/3
electrical energy used = 1.46 *10^5 J
the electrical energy is usde to freeze the ice is 1.46 *10^5 J
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total energy dumped in kitehen = electrical energy used + thermal energy removed
total energy dumped in kitehen = 1.46 *10^5 J + 4.39 *10^5 J
total energy dumped in kitehen = 5.85 *10^5 J
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specific heat of air , Sa = 0.2 * cal/(gm.degree C)
Sa = 0.2 * 4186 J/(kg.degree)
Sa = 837.2 J/(Kg.degree C)
heat = m * Sa * del T
5.85 *10^5 = 40 * 837.2 * del T
del T = 17.5 degree C
the temperature will rise is 17.5 degree C
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efficiency of feezer = 1 J/(3 J) * 1000
efficiency of feezer = 33.3 %
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