Question

The work done in erg for the reversible expansion of $1mole$ of an ideal gas from a volume of $10litres$ to $20litres$ at ${25}^{o}C$ is

• A. $2.303\times 298\times 0.082log2$
• B. $-298\times {10}^7\times 8.314\times 2.303log2$
• C. $-2.303\times 298\times 0.082log0.5$
• D. $2.303\times 298\times 2log2$

Answer 1

The correct option is B $-298\times {10}^7\times 8.314\times 2.303log2$

for isothermal process,
$W_{rev}=-2.303nRTlog\frac{V_2}{V_1}$
$=-2.303\times 1\times 0.0821\times 298log\frac{20}{10}$
$=-2.303\times 0.0821\times 298\times log2Latm$
or $W_{rev}=-2.303\times 8.314\times 298\times log2J$
$=-2.303\times 8.314\times {10}^7\times 298\times log2erg$