Question

1 mole of an ideal gas expands isothermally so that its pressure falls $1.0 \times {{10}^{5}}$ Pa to $0.5\times {{10}^{5}}$ Pa. The change in entropy of the gas is equal to

• A. 0
• B. 0.693 J/K
• C. 5.76 J/K
• D. None of these

Answer 1

Answer: (C)

5.76 J/K

Answer 2

Given that $n=1$ mol $p_{1}=1.0 \times 10^{5} Pa$
$p_{2}=0.5 \times 10^{5} Pa$
Change in entropy of the gas $=\frac{Q}{T}$
$=\frac{W}{T}=\frac{n R T \log \left(p_{1} / p_{2}\right)}{T}$
$=n R \log \left(p_{1} / p_{2}\right)$
$=1 \times 8.31 \times 2.303 \times 0.3010$
$=5.76\, J / K$