A vessel containing 10 kg of water is left out where it evaporates. If the temperature remains constant at 20°C, what is the change in entropy (in kcal/K)? (The latent heat of vaporization at 20°C is 585 cal/g.)
A) 30
B) 10
C) 20
D) 40
E) 290

Question

Quizplus · Accepted Answer

The change in entropy can be calculated using the formula ΔS = Q/T, where Q is the heat transferred and T is the temperature at which the transfer occurs. In this case, the heat transferred is the latent heat of vaporization, which can be calculated as:

Q = mL = (10 kg)(1000 g/kg)(585 cal/g) = 5.85 x 10^6 cal

Since we want the change in entropy in units of kcal/K, we need to convert the heat transferred from calories to kcal:

Q = 5.85 x 10^6 cal = 5850 kcal

Therefore, the change in entropy is:

ΔS = Q/T = (5850 kcal)/(293 K) = 19.93 kcal/K, which is closest to 20 kcal/K (Choice C).

A Vessel Containing 10 Kg of Water Is Left Out