A substance has a melting point of 20°C and a heat of fusion of 3.5 × 10⁴ J/kg. The boiling point is 150°C and the heat of vaporization is 7.0 × 10⁴J/kg at a pressure of 1.0 atm. The specific heats for the solid, liquid, and gaseous phases are 600 J/(kg∙K), 1000 J/(kg∙K), and 400 J/(kg∙K), respectively. The quantity of heat given up by 0.50 kg of the substance when it is cooled from 170°C to 88°C, at a pressure of 1.0 atmosphere, is closest to A) 70 kJ. B) 14 kJ. C) 21 kJ. D) 30 kJ. E) 44 kJ.

Question

Quizplus · Accepted Answer

The correct answer is A.The heat given up by the substance when it is cooled from 170°C to 88°C is equal to the heat of vaporization plus the heat of fusion plus the heat capacity of the solid and liquid phases. The heat of vaporization is 7.0 × 10^4 J/kg, the heat of fusion is 3.5 × 10^4 J/kg, the heat capacity of the solid phase is 600 J/(kg∙K), and the heat capacity of the liquid phase is 1000 J/(kg∙K). The temperature change is 170°C - 88°C = 82°C. Therefore, the heat given up by the substance is:Q = (7.0 × 10^4 J/kg) + (3.5 × 10^4 J/kg) + [(600 J/(kg∙K)) × (82°C)] + [(1000 J/(kg∙K)) × (82°C)]= 70,000 J/kgTherefore, the quantity of heat given up by 0.50 kg of the substance is:Q = (70,000 J/kg) × (0.50 kg)= 35,000 J= 35 kJTherefore, the correct answer is A.

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