A substance has a melting point of 20°C and a heat of fusion of 3.4 × $10 ^ { 4 }$ J/kg. The boiling point is $150 ^ { \circ } \mathrm { C }$ and the heat of vaporization is $6.8 \times 10 ^ { 4 } \mathrm {~J} / \mathrm { kg }$ 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 required to raise the temperature of $1.90 \mathrm {~kg}$ of this substance from $- 4 ^ { \circ } \mathrm { C }$ to $106 ^ { \circ } \mathrm { C }$ at a pressure of one atmosphere?
A)260 kJ
B)190 kJ
C)230 kJ
D)92 kJ
E)320 kJ

Question

Quizplus · Accepted Answer

The heat required to raise the temperature of the substance from -4°C to 20°C is:$$Q_1 = mc_s \Delta T = (1.90 \mathrm{~kg})(600 \mathrm{~J/kg \cdot K})(20°C - (-4°C)) = 228 \mathrm{~kJ}$$The heat required to melt the substance at 20°C is:$$Q_2 = mL = (1.90 \mathrm{~kg})(3.4 	imes 10^4 \mathrm{~J/kg}) = 64.6 \mathrm{~kJ}$$The heat required to raise the temperature of the liquid from 20°C to 100°C is:$$Q_3 = mc_l \Delta T = (1.90 \mathrm{~kg})(1000 \mathrm{~J/kg \cdot K})(100°C - 20°C) = 152 \mathrm{~kJ}$$The heat required to vaporize the substance at 100°C is:$$Q_4 = mL = (1.90 \mathrm{~kg})(6.8 	imes 10^4 \mathrm{~J/kg}) = 129.2 \mathrm{~kJ}$$The heat required to raise the temperature of the gas from 100°C to 106°C is:$$Q_5 = mc_g \Delta T = (1.90 \mathrm{~kg})(400 \mathrm{~J/kg \cdot K})(106°C - 100°C) = 23.2 \mathrm{~kJ}$$The total heat required is:$$Q = Q_1 + Q_2 + Q_3 + Q_4 + Q_5 = 228 \mathrm{~kJ} + 64.6 \mathrm{~kJ} + 152 \mathrm{~kJ} + 129.2 \mathrm{~kJ} + 23.2 \mathrm{~kJ} = 597 \mathrm{~kJ}$$Therefore, the correct answer is A.

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