Question

One mole of an ideal gas expands isothermally and reversibly at ${25}^{o}C$ from a volume of 10 litres to a volume of 20 litres. What is the change in entropy of the gas?

• A. $5.76J{K}^{-1}$
• B. $8.54J{K}^{-1}$
• C. $-5.76J{K}^{-1}$
• D. $-8.54J{K}^{-1}$

Answer 1

The correct option is A $5.76J{K}^{-1}$

$n=1,R=8.314J{K}^{-1}mo{l}^{-1},V_2=20L,V_1=10L$
we know that
$△S=2.303n{C}_{v}log\frac{T_2}{T_1}+2.303nRlog\frac{V_2}{V_1}$
for isothermal process, $T_1=T_2$
$\therefore △S=2.303nRlog\frac{V_2}{V_1}$
$=2.303\times 1\times 8.314\times log\frac{20}{10}=5.76J{K}^{-1}$