2 moles of an ideal gas expands isothermally at 300 K from an initial volume V to a final volume 2V . Let W_ rev be the work done when the expansion is carried out reversibly, and W_ irr be the work done when the expansion is carried out irreversibly against a constant external pressure equal to the final pressure of the gas. The magnitude of the difference between the work done in these two processes, |W_ rev | - |W

Step-by-step solution

For the reversible isothermal expansion: |W_ rev | = nRT ( V₂ V₁ ) |W_ rev | = 2 8.3 300 (2) |W_ rev | = 4980 0.7 = 3486 J For the irreversible isothermal expansion: The external pressure is equal to the final pressure of the gas, P_ final = nRT 2V . |W_ irr | = P_ ext V |W_ irr | = ( nRT 2V ) (2V - V) |W_ irr | = nRT 2 |W_ irr | = 2 8.3 300 2 = 2490 J The magnitude of the difference in work done is: |W_ rev | - |W_ irr | = 3486 - 2490 = 996 J Answer: 996