## Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (3rd Edition)

a) $V_{2}$ = $V_{1}$ b) $T_{2}$ =$\frac{T_{1}}{3}$
a) This is an isochoric process, which means that volume remains constant. Thus $V_{2}$ = $V_{1}$ b) For this question, we can use the ideal gas law: $\frac{p_{1}V_{1}}{T_{1}}$ = $\frac{p_{2}V_{2}}{T_{2}}$, where: $p_{1}$ is the initial pressure $p_{2}$ is the final pressure $T_{1}$ is the initial temperature $T_{2}$ is the final temperature $V_{1}$ is the initial volume $V_{2}$ is the final volume. So now we solve for $T_{2}$: $T_{2}$ = $\frac{p_{2}V_{2}T_{1}}{p_{1}V_{1}}$ = $\frac{\frac{1}{3}p_{1}V_{1}T_{1}}{p_{1}V_{1}}$ = $\frac{1}{3}T_{1}$ = $\frac{T_{1}}{3}$