# Five moles of an ideal gas at 1 bar and 298 k is expanded into vacuum to double the volume.

Question:

Five moles of an ideal gas at 1 bar and $298 \mathrm{~K}$ is expanded into vacuum to double the volume. The work done is :

1. $\mathrm{C}_{\mathrm{V}}\left(\mathrm{T}_{2}-\mathrm{T}_{1}\right)$

2. $-\mathrm{RT}\left(\mathrm{V}_{2}-\mathrm{V}_{1}\right)$

3. $-R T \ln V_{1} / V_{1}$

4. zero

Correct Option: , 4

Solution:

In expansion against vacuum

$P_{\text {ext }}=0$

$W=-P_{\text {ext }} \Delta V=0$

w = 0