Question

In an irreversible isothermal expansion of 2 moles of an ideal gas, work done (W) is found to be (-P\(_{ext}\)V). If the same isothermal expansion is carried out reversibly, the work done will be:

• A. -0.683 RT
• B. -1.386 RT
• C. -0.3010 RT
• D. 0

Hint:

When dealing with isothermal processes, remember that the work done in reversible and irreversible processes are related by a factor of \( 2.303 \) in the case of isothermal expansion.

Answer 1

The Correct Option is B

For an irreversible expansion, the work done \( W \) is given by: \[ W = -P_{ext} \Delta V \] For a reversible expansion, the work done is given by: \[ W = -nRT \ln \left( \frac{V_f}{V_i} \right) \] For the same isothermal expansion, the relationship between irreversible and reversible work done is: \[ W_{reversible} = W_{irreversible} \times 2.303 \] Thus: \[ W_{reversible} = -2.303 \times W_{irreversible} = -2.303 \times (-1 \cdot 2RT) = -1.386 RT \]