First law of thermodynamics: A cylinder contains 24.0 moles of an ideal gas at a temperature of 300 K. The gas is compressed at constant pressure until the final volume equals 0.63 times the initial volume. The molar heat capacity at constant volume of the gas is 24.0 J/mol · K and the ideal gas constant is R = 8.314 J/mol ∙ K. The change in the internal (thermal) energy of the gas is closest to

Question

Quizplus · Accepted Answer

The change in internal energy (ΔU) for an ideal gas is given by ΔU = nCvΔT. Since the process is at constant pressure, we can use the relation ΔT = (PΔV)/(nR). Given that the final volume is 0.63 times the initial volume, ΔV = V_initial - 0.63V_initial = 0.37V_initial. Using the ideal gas law, P = nRT/V, we find ΔT = (0.37V_initial * nR)/(nR * V_initial) = 0.37T_initial. Thus, ΔU = nCv(0.37T_initial) = 24.0 moles * 24.0 J/mol·K * 0.37 * 300 K = -64,080 J = -64 kJ.

First Law of Thermodynamics: a Cylinder Contains 24