Question

$6$ moles of an ideal gas expand isothermally and reversibly from a volume of $1litre$ to a volume of $10litres$ at ${27}^{\circ }C$. What is the maximum work done?

• A. $-47kJ$
• B. $-100kJ$
• C. $0$
• D. $-34.465kJ$

Answer 1

The correct option is D $-34.465kJ$

For isothermal Process,

$W=-{\int }_{V_1}^{V_2}PdV=-{\int }_{V_1}^{V_2}\frac{nRT}{V}dV=-nRTln\left(\frac{V_2}{V_1}\right)$

$W=-2.303nRT\log \frac{V_2}{V_1}$

Given $n=6,T={27}^{\circ }C=273+27=300K$

$V_1=1L,V_2=10L$

$W=-2.303\times 6\times 8.314\times 300\log \frac{10}{1}$

$=-34.465kJ$

Hence, option D is correct