Question

Two liters of an ideal gas at a pressure of $10atm$ expands isothermally at ${25}^{\circ }C$ into a vacuum until its total volume is $10\text{liters}.$ How much heat is absorbed and how much work is done in the expansion?

Answer 1

Step 1: Work done

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

$W=-P_{ext}.△V$

As the gas is expanding is vacuum which has no pressure, i.e., $P_{ext.}=0$

$\therefore W=0$

Hence, no work is done.

Step 2: Absorbed heat

We know from first law of thermodynamics,

$△U=q+W$

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

$\therefore △U=0$

Hence, $q=-W=0$

Therefore, no heat is absorbed in the expansion.

Final answer:

No work is done, and no heat is absorbed in the expansion