Question

The work done by an ideal gas of 2 moles in increasing its volume from \( V \) to \( 2V \) at constant temperature \( T \) is \( W \). The work done by an ideal gas of 4 moles in increasing its volume from \( V \) to \( 8V \) at constant temperature \( \frac{T}{2} \) is

• A. \( W \)
• B. \( 2W \)
• C. \( 3W \)
• D. \( 4W \)

Hint:

For isothermal expansion, work done is proportional to the number of moles and logarithm of the volume ratio.

Answer 1

The Correct Option is C

The work done in an isothermal process is given by: \[ W = nRT \ln \frac{V_f}{V_i} \] For the first process: \[ W = 2RT \ln 2 \] For the second process: \[ W' = 4 \times \frac{T}{2} \ln 8 \] \[ = 2RT \ln 8 \] \[ = 2RT \ln (2^3) = 2RT \times 3 \ln 2 = 3 \times 2RT \ln 2 \] \[ = 3W \] Thus, the correct answer is 3W.