To raise the temperature of 1 mole of an ideal gas from 400 K to 500 K, how much heat is required if — Thermodynamics and Thermochemistry Chemistry Question

💡 Solution & Explanation

The heat required at constant pressure is $q_p = \Delta H = \int_{T_1}^{T_2} n C_p dT$. Substituting the values: $q_p = \int_{400}^{500} 1 \times (3 + 1.2 \times 10^{-3} T) dT = [3T + \frac{1.2 \times 10^{-3} T^2}{2}]_{400}^{500} = 3(500 - 400) + 0.6 \times 10^{-3} (500^2 - 400^2) = 300 + 0.6 \times 10^{-3} (250000 - 160000) = 300 + 0.6 \times 10^{-3} (90000) = 300 + 54 = 354 \text{ cal}$.