A chemist cools 75.0 g of methanol vapor initially at 80 °C and 1 atm until the…
PHYSICS · Multi-part · ISC · Physics · Heat and Thermodynamics · Physical World and Measurement
Problem
A chemist cools 75.0 g of methanol vapor initially at 80 °C and 1 atm until the sample reaches 0 °C at the same pressure. The process occurs in three distinct stages that have been characterized experimentally:
• Stage I (80 °C → 78 °C): The temperature of the vapor decreases linearly while 2.0 kJ of heat is released.
• Stage II (78 °C plateau): The temperature remains constant while the vapor condenses completely to liquid; heat is released at a constant rate of 550 J s⁻¹ for 90 s.
• Stage III (78 °C → 0 °C): The temperature of the liquid decreases, releasing an additional 14.0 kJ of heat.
(a) Calculate the quantity of heat released during Stage II. Include the proper sign in your answer.
(b) Combine the data from all three stages to determine the total heat exchanged, qtotal, for the entire cooling process. Report both sign and magnitude.
(c) Discuss why the temperature of the methanol remains constant during Stage II even though heat is continually released. Your explanation should relate molecular interactions to enthalpy changes.
(d) If the entire process were reversed—warming the same 75.0 g sample from 0 °C back to 80 °C at 1 atm—describe qualitatively how the algebraic sign and magnitude of qtotal would compare with the value obtained in part (b). Justify your answer.