A substance has a melting point of 20°C and a heat of fusion of $3.6 \times 10^4 \mathrm {~J} / \mathrm { kg }$ The boiling point is $150 ^ { \circ } \mathrm { C }$ and the heat of vaporization is $7.2 \times 10^4 \mathrm {~J} / \mathrm { kg }$ at a pressure of one atmosphere. The specific heats for the solid, liquid, and gaseous phases are 600 J/kg ∙ K (solid), 1000 J/kg ∙ K (liquid), and 400 J/kg ∙ K (gaseous). How much heat is given up by $2.80 \mathrm {~kg}$ of this substance when it is cooled from 170°C to 86°C at a pressure of one atmosphere?
A) 400 kJ
B) 200 kJ
C) 300 kJ
D) 440 kJ
E) 640 kJ

Question

Quizplus · Accepted Answer

The heat given up is the sum of the heat lost in cooling the gas to the boiling point, the heat of vaporization, the heat lost in cooling the liquid to the melting point, and the heat of fusion.$$Q = mc_s (T_b - T_i) + mL + mc_l (T_m - T_b) + mf$$$$Q = (2.80 \mathrm {~kg})(600 \mathrm {~J} / \mathrm {~kg} \cdot \mathrm {~K})(150 ^ { \circ } \mathrm { C } - 170 ^ { \circ } \mathrm { C }) + (2.80 \mathrm {~kg})(7.2 	imes 10^4 \mathrm {~J} / \mathrm { kg }) + (2.80 \mathrm {~kg})(1000 \mathrm {~J} / \mathrm {~kg} \cdot \mathrm {~K})(150 ^ { \circ } \mathrm { C } - 86 ^ { \circ } \mathrm { C }) + (2.80 \mathrm {~kg})(3.6 	imes 10^4 \mathrm {~J} / \mathrm { kg })$$$$Q = 400 \mathrm {~kJ}$$

A Substance Has a Melting Point of 20°C and a Heat