Question

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

• A. Zero
• B. ${\mathrm{C}}_{\mathrm{v}}[{\mathrm{T}}_2-{\mathrm{T}}_1]$
• C. $-\mathrm{RT}({\mathrm{V}}_2-{\mathrm{V}}_1)$
• D. $-\mathrm{RT}\ln ({\mathrm{V}}_2/{\mathrm{V}}_1)$

Answer 1

The correct option is A

Zero

Answer: (A)

Explanation for correct option:

From the formula of workdone,

$\mathrm{W}=-{\mathrm{P}}_{\mathrm{ext}}∆\mathrm{V}$

In expansion against vaccum, ${\mathrm{P}}_{\mathrm{ext}}=0$

Hence,

$\mathrm{W}=0$

As it is free expansion against zero external pressure, work done is zero.

Hence option (A) is the correct option.