Question

Expansion of a gas in vacuum is called free expansion. Calculate the work done and the change in internal energy when $1$ liter of ideal gas expands isothermally into vacuum unit its total volume is $5$ litre?

Answer 1

Work done in vacuum is calculated by:

$w=-P_{ext}(V_{final}–V_{initial})$

For the given problem: $P_{ext}=0$, because it is a free expansion (in the vacuum).

Hence,

$w=-(0\times (5-1\left)\right)$

$w=0$

According to joule experimental observation, For an isothermal expansion of ideal gas, no heat will be absorbed or evolved, hence $q=0$

By the $1^{st}$ law of thermodynamics,

$q+w=\Delta U$

$\Delta U=0$

Since, $w=0$ and $q=0$, then the change in internal energy $\Delta U$ will also be $0$.