Assume a material has a heat of polymerization of -1000 kJ/kg, an average heat capacity of 2 kJ/kg-K, and the starting temperature of the material is 200 K. What is the maximum adiabatic temperature that could be reached by the polymerization of the material?

Assume a material has a heat of polymerization of -1000 kJ/kg, an average heat capacity of 2 kJ/kg-K, and the starting temperature of the material is 200 K. What is the maximum adiabatic temperature that could be reached by the polymerization of the material?

• A. -200 K
• B. -300 K
• C. -700 K
• D. -400 K

Answer: (C)

Under adiabatic conditions, all the heat released by the polymerization stays in the material, so it heats up rather than losing energy to the surroundings. The heat released per kilogram is 1000 kJ/kg (the magnitude of the heat of polymerization). The temperature rise is the heat added per kilogram divided by the material’s heat capacity per kilogram: DeltaT = q/Cp = 1000 kJ/kg / 2 kJ/kg-K = 500 K. Starting from 200 K, the maximum adiabatic temperature the material could reach is 200 K + 500 K = 700 K. The result shows a final temperature of 700 K; the option with a negative sign would imply cooling, which isn’t consistent with an exothermic, adiabatic heat release.

Under adiabatic conditions, all the heat released by the polymerization stays in the material, so it heats up rather than losing energy to the surroundings. The heat released per kilogram is 1000 kJ/kg (the magnitude of the heat of polymerization). The temperature rise is the heat added per kilogram divided by the material’s heat capacity per kilogram: DeltaT = q/Cp = 1000 kJ/kg / 2 kJ/kg-K = 500 K. Starting from 200 K, the maximum adiabatic temperature the material could reach is 200 K + 500 K = 700 K. The result shows a final temperature of 700 K; the option with a negative sign would imply cooling, which isn’t consistent with an exothermic, adiabatic heat release.