Phase changes: 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 × 10⁴ J/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 heat given up by the substance when it is cooled from 170°C to 88°C is the sum of the heat given up when it condenses and the heat given up when it cools in the liquid phase. The heat given up when it condenses is:$$Q_1 = m 	imes L_v = 0.50 	ext{ kg} 	imes 7.0 	imes 10^4 	ext{ J/kg} = 3.5 	imes 10^4 	ext{ J}$$The heat given up when it cools in the liquid phase is:$$Q_2 = m 	imes c_l 	imes (T_2 - T_1) = 0.50 	ext{ kg} 	imes 1000 	ext{ J/(kg ∙ K)} 	imes (88°C - 150°C) = -31 	ext{ kJ}$$The total heat given up is:$$Q = Q_1 + Q_2 = 3.5 	imes 10^4 	ext{ J} - 31 	ext{ kJ} = -27.5 	ext{ kJ}$$The closest answer choice is A) 70 kJ.

Phase Changes: a Substance Has a Melting Point of 20°C