91影视

The relation between pressure, volume, temperature and number of moles is expressed by the ideal gas equationPV=nRT.

In the first case, the volume and the number of moles is kept constant. Rearranging the equation,$P=\frac{nR}{V}T$, which means, $P=acons\tan t*T$or $P鈭�T$. So, as there are two cases before cooling() and after cooling($P_1,T_1$), then it becomes, $\frac{P_1}{T_1}=\frac{P_2}{T_2}$.

Thus, the relation for final temperature is $T_2=\frac{P_2{T}_1}{P_1}$.

In the second case, the pressure $P_1$and volume $V_2$are changed, to $P_3$and $V_3$, with temperature and number of moles kept constant. Then, ideal gas equation is arranged as $V=\frac{nRT}{P}$which implies,$V鈭�\frac{1}{P}$or $PV=acons\tan t$. For the two cases, $P_2{V}_2=P_3{V}_3$. Thus, the final volume $V_3=\frac{P_2{V}_2}{P_3}$.

In degree Celsius,$T_2=97.67K-273=-175.{33}^{o}C.$.

Hence, the final temperature when the tank is kept at a constant volume is $-175.{33}^{o}C.$

(b)The final volume is found from $V_3=\frac{P_2{V}_2}{P_3}$.

Substituting the values of $P_2=1atm,V_2=3L\left(provided\right),P_3=3atm$ in $V_3=\frac{P_2{V}_2}{P_3}$,

localid="1668075026754" $$\begin{gathered} V_3=\frac{1*3}{3} \\ {V}_3=1 \end{gathered}$$

Hence, the final volume after final compression to 3atm is 1L.