Question

Two litres of an ideal gas at a pressure of 10 atm, expands isothermally into vacuum until its total volume is 10 litres. How much heat is absorbed and how much work is done in the expansion?

Answer 1

In case of expansion, work is done by the system.

Now, as we know that,

$W=-P_{ext.}\Delta V$

As the gas is expanding is vaccum which has no pressure, i.e.,

$p_{ext.}=0$

$\therefore W=0$

Hence no work is done.

From first law of thermodynamics,

$\Delta U=q+W$

As the system is working at constant temperature, i.e., isothermally.

$\therefore \Delta U=0$

Hence $q=-W=0$

Hence no heat is absorbed in the expansion.