(Solved): The gas law for an ideal gas at absolute temperature \( T \) (in kelvins), pressure \( P \) (in at ...

The gas law for an ideal gas at absolute temperature \( T \) (in kelvins), pressure \( P \) (in atmospheres), 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, \( P=8.0 \) atm and is increasing at a rate of \( 0.14 \) atm \( / \mathrm{min} \) and \( V=12 \mathrm{~L} \) and is decreasing at a rate of \( 0.16 \mathrm{~L} / \mathrm{min} \). Find the rate of change of \( T \) with respect to time (in \( \mathrm{K} / \mathrm{min} \) ) at that instant if \( n=10 \) mol. (Round your answer to four decimal places.) \[ \frac{d T}{d t}=\quad \& \mathrm{~K} / \min \]