A tub containing 10 kg of cold water at 4° C is placed in a garage on a winter e

Question

A tub containing 10 kg of cold water at 4° C is placed in a garage on a winter evening to keep the garage warm. If 1.5 kg of water freezes overnight, which of the following is correct?

A. The entrophy of the water increases by approximately 2400 J/K

B. The entrophy of the water does not change, since the freezing is a reversible process

C. The entrophy of the water decreases by approximately 1800 J/K

D. The entrophy of the water increases by approximately 1800 J/K

E. The entrophy of the water decreases by approximately 2400 J/K

I know the entrophy decreases, and the answer is supposed to be E, but could someone give me a hand with the math behind it?

Explanation / Answer

The water must go from 4oC to 0o C and release heat

Q = mcT

Q = (10)(4186)(4)

Q = 1.67 X 105 J of heat

Then 1.5 grams of the water freezes, so by the latent heat of fusion,

Q = mHf

Q = (1.5)(3.33 X 105)

Q = 5 X 105 J

Total heat lost = 1.67 X 105 + 5 X 105 = 6.67 X 105 J

Then, for entropy, S = Q/T

Since this occurs at 0 Celsius, this is 273.15 K

So 6.67 X 105 J/273.15 = 2440 J/K

By rounding, you can see that that is 2400 J/K

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