Chemistry - Thermodynamics - I Question with Solution | TestHub

$\mathrm{n}=5, \mathrm{T}=293 \mathrm{K}=\mathrm{const},\mathrm{\Delta U}=0$

${\mathrm{P}}_1=2.1 \mathrm{MPa},{\mathrm{P}}_2=1.3 \mathrm{MPa}$

${\mathrm{P}}_{\mathrm{ext}}=4.3 \mathrm{MPa}=\mathrm{const}.$

$\mathrm{W}=-{\mathrm{P}}_{\mathrm{ext}}\left({\mathrm{V}}_2-{\mathrm{V}}_1\right)=-{\mathrm{P}}_{\mathrm{ext}}\left(\frac{\mathrm{nRT}}{{\mathrm{P}}_2}-\frac{\mathrm{nRT}}{{\mathrm{P}}_1}\right)$

or, $\mathrm{W}=-{\mathrm{P}}_{\mathrm{ext}}\mathrm{nRT}\left(\frac{1}{{\mathrm{P}}_2}-\frac{1}{{\mathrm{P}}_1}\right)$

$=-4.3\times 5\times 8.314\times 293\left(\frac{1}{1.3}-\frac{1}{2.1}\right)$

$=-4.3\times 5\times 8.314\times 293\left(\frac{2.1-1.3}{1.3\times 2.1}\right)$

$=-15347.7 \mathrm{J}$

or, $\mathrm{W}=-15.35 \mathrm{kJ}$

$\Delta {\mathrm{U}}^0=\mathrm{q}+\mathrm{W}$

$\therefore \mathrm{q}=-\mathrm{W}$

or, $\mathrm{q}=15.35 \mathrm{kJ}$ (for $5$ moles)

$\therefore \mathrm{q}/\mathrm{mole}=\frac{15.35}{5}=3 \mathrm{kJ} {\mathrm{mol}}^{-1}$