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
A) -64 kJ.
B) -86 kJ.
C) 64 kJ.
D) 86 kJ.
E) -22 kJ.

Question

Quizplus · Accepted Answer

The change in internal energy is given by:$$\Delta U = nC_v\Delta T$$where n is the number of moles, $C_v$ is the molar heat capacity at constant volume, and $\Delta T$ is the change in temperature.In this case, the pressure is constant, so the change in temperature is given by:$$\Delta T = \frac{P\Delta V}{nR}$$where P is the pressure, $\Delta V$ is the change in volume, and R is the ideal gas constant.Substituting these equations into the first equation, we get:$$\Delta U = nC_v\frac{P\Delta V}{nR}$$$$\Delta U = C_v\frac{P\Delta V}{R}$$$$\Delta U = (24.0 	ext{ J/mol} \cdot 	ext{K})\frac{(1 	ext{ atm})(0.63 	ext{ L}-1 	ext{ L})}{0.0821 	ext{ L} \cdot 	ext{atm/mol} \cdot 	ext{K}}$$$$\Delta U = -64 	ext{ kJ}$$Therefore, the change in internal energy is closest to -64 kJ.

A Cylinder Contains 24