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  4. One mole of O 2 gas having a volume equal to 22.4 litre at 0° C and 1 atmospheric pressure is compressed isothermally so that its volume reduces to 11.2 litre. The work done in this process is nearly:

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Q. One mole of $O _{2}$ gas having a volume equal to $22.4$ litre at $0^{\circ} C$ and $1$ atmospheric pressure is compressed isothermally so that its volume reduces to $11.2$ litre. The work done in this process is nearly:

Kinetic Theory

Solution:

Work done in isothermal process is given by
$W=2.303\, n R T \log _{10}\left(\frac{V_{f}}{V_{i}}\right)$
$W=2.303 \times 1 \times 8.314 \times 273 \times \log _{10}\left(\frac{11.2}{22.4}\right)$
$W=-1573.5\, J$
$W \approx-1570\, J$