A 40.0-L container is divided into two equal parts by a rubber membrane. One half of the container has $1.50$ moles of an ideal monatomic gas at $250 \mathrm {~K}$, and the other half is a vacuum. The container is well insulated, so there is no exchange of heat with the surroundings. The membrane breaks, and eventually the gas reaches a new equilibrium condition occupying the entire volume. What is the final temperature of the gas?
A) $125 \mathrm {~K}$
B) $100 \mathrm {~K}$
C) $157 \mathrm {~K}$
D) $180 \mathrm {~K}$
E) $250 \mathrm {~K}$

Question

Quizplus · Accepted Answer

Since the container is well insulated and there is no heat exchange with the surroundings, the process is adiabatic. The internal energy of an ideal gas depends only on its temperature, not on its volume or pressure. Therefore, if the internal energy of the gas doesn't change (no heat is added or removed), the temperature of the gas remains constant at $250 \mathrm{K}$ after the expansion.

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