Chemistry - Thermodynamics - I Question with Solution | TestHub

For $n=5$, $T=293K=const$, and $\Delta U=0$.

$P_1=2.1MPa$, $P_2=1.3MPa$.

$P_{ext}=4.3MPa=const$.

$W=-P_{ext}(V_2-V_1)=-P_{ext}\left(\frac{nRT}{P_2}-\frac{nRT}{P_1}\right)$

or, $W=-P_{ext}nRT\left(\frac{1}{P_2}-\frac{1}{P_1}\right)$

$$\begin{array}{rl}& =-4.3\times 5\times 8.314\times 293\left(\frac{1}{1.3}-\frac{1}{2.1}\right)\\ & =-4.3\times 5\times 8.314\times 293\left(\frac{2.1-1.3}{1.3\times 2.1}\right)\\ & =-15347.7J\end{array}$$

or, $W=-15.35kJ$. Since $\Delta U=q+W$, then $q=-W$.

Therefore, $q=15.35kJ$ (for 5 moles).

Thus, $q/mole=\frac{15.35}{5}=3kJmo{l}^{-1}$.