Problem 33E

33. The gas law for an ideal gas at absolute temperature $T$ (in kelvins), pressure $P$ (in atmospheres, atm), and volume $V$ (in liters) is $P V=n R T$, where $n$ is the number of moles of the gas and $R=0.0821$ is the gas constant. Suppose that, at a certain instant, $P=8.0 \mathrm{~atm}$ and is increasing at a rate of $0.10 \mathrm{~atm} / \mathrm{min}$ and $V=10 \mathrm{~L}$ and is decreasing at a rate of $0.15 \mathrm{~L} / \mathrm{min}$. Find the rate of change of $T$ with respect to time at that instant if $n=10$ moles.