The work done during reversible isothermal expansion of one mole of hydrogen gas at \(25^\circ C\) from pressure of 20 a…

For isothermal reversible expansion:

\(W=−nRT\ln ⁡(\frac{{P}_{1}}{{P}_{2}})\)

\(W=−1\times 2\times 298\times \ln ⁡(\frac{20}{10})=−596\times \ln ⁡(2)\\ =−596\times (0.693)=–413.14\text{ }\text{cal}\)

OR

\(W=−2.303n\text{ }RT\text{ log}\left(\frac{{P}_{1}}{{P}_{2}}\right)\)

\(=−2.303\times 1\times 2\times 298\times \text{log}\frac{20}{10}\)

\(=−2.303\times 596\times \text{log}2\)

\(=−2.303\times 596\times 0.3010\)

\(W=−413.14\text{ calories }\)