A cylinder contains 13 moles of an ideal gas at a temperature of 300 K. The gas is compressed at constant pressure until the final volume equal 0.70 times the initial volume. The molar heat capacity at constant volume of the gas is 24.0 J/mol ∙ K. What is the change in the internal (thermal) energy of the gas during this process? (R = 8.31 J/mol ∙ K)
A) -28 kJ
B) -38 kJ
C) 28 kJ
D) 38 kJ
E) -9.7 kJ

Question

Quizplus · Accepted Answer

The change in internal energy for an ideal gas is given by ΔU = nCvΔT. Since the process is at constant pressure, we can use the relation ΔT = (PΔV)/(nR). The change in volume is ΔV = V_final - V_initial = 0.70V_initial - V_initial = -0.30V_initial. Substituting these into the equation for ΔU, we get ΔU = nCv(PΔV)/(nR) = CvPΔV/R. Given Cv = 24.0 J/mol∙K, PΔV = -0.30nRT, and R = 8.31 J/mol∙K, we find ΔU = 13 * 24 * (-0.30 * 13 * 8.31 * 300) / 8.31 = -28,000 J = -28 kJ.

A Cylinder Contains 13 Moles of an Ideal Gas at a Temperature