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  4. The volume of one mole of an ideal gas changes from V to 2 V at temperature 300 K. If R is universal gas constant, then work done in this process is

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Q. The volume of one mole of an ideal gas changes from $V$ to $2\, V$ at temperature $300 \,K$. If $R$ is universal gas constant, then work done in this process is

Thermodynamics

Solution:

Work done in an isothermal process
$W=n R T \ln \left(\frac{V_{2}}{V_{1}}\right)$
Here, $n=1$ mol, $T=300\, K$ ,
$ V_{1}=V$ and $V_{2}=2 V$
$\therefore W=1 \times R \times 300 \ln \left(\frac{2 V}{V}\right)$
$=300 R \ln 2$