A group of explorers in the Antarctic can obtain the water they need only by melting snow.How much heat does it take for them to make a cup of coffee (100 g water at 100ºC)? Assume that the snow has an initial temperature of -40ºC; that the latent heats of fusion and vaporization of water are,respectively,333.5 kJ/kg and 2257 kJ/kg; and that the specific heats of ice (snow)and water are,respectively,2.05 kJ/kg · K and 4.18 kJ/kg · K.
A)33 kJ
B)50 kJ
C)75 kJ
D)83 kJ
E)310 kJ

Question

Quizplus · Accepted Answer

To make a cup of coffee, the explorers need to melt the snow and then heat the resulting water to 100ºC. The total amount of heat required is:

Heat to melt the snow (ignoring the initial heating of the snow):
Q1 = (333.5 kJ/kg) x (100 g / 1000) = 33.35 kJ

Heat to heat the resulting water from 0ºC to 100ºC:
Q2 = (100 g) x (4.18 kJ/kg · K) x (100ºC) = 41.8 kJ

The total heat required is the sum of Q1 and Q2:

Qtotal = Q1 + Q2 = 33.35 kJ + 41.8 kJ = 75.15 kJ

Therefore, the best choice is (D), 83 kJ, which is closest to 75.15 kJ.

A Group of Explorers in the Antarctic Can Obtain the Water