Question

Entropy change when $4$ moles of an ideal gas expands reversibly from an initial volume of $1{\text{dm}}^3$ to a final volume of $10{\text{dm}}^3$ at a constant temperature of $298\text{K}$ is:

• A. $5705.8{\text{J K}}^{-1}$
• B. $76.58{\text{J K}}^{-1}$
• C. $\mathrm{38..29}{\text{J K}}^{-1}$
• D. $-19.15{\text{J K}}^{-1}$

Answer 1

The correct option is B $76.58{\text{J K}}^{-1}$

$\Delta S=\frac{q_{rev}}{T}$
For isothermal reversible change,
$n=4\text{moles,}{V}_1=1{\text{dm}}^3\text{and}{V}_2=10{\text{dm}}^3\therefore \Delta S=2.303nR\log \frac{V_2}{V_1}\therefore \Delta S=2.303nR\log \frac{10}{1}=2.303\times 4\text{mol}\times 8.314{\text{J K}}^{-1}\therefore \Delta S=76.58{\text{J K}}^{-1}$