Question

An ideal gas is allowed to expand against a constant pressure of 2 bar from 1 L to 50 L in one step. Calculate the amount of work done by the gas. If the same expansion were carried out reversibly, will the work done be higher or lower than the earlier case? [Given that 1 L bar = 100 J]

Answer 1

Given,

Pressure (P) = 2 bar

Initial volume $(V_1)$ = 1 L

Final volume $(V_2)$ = 50 L

Amount of work done by the gas = (- pressure) × (final volume - initial volume)

= (-2 bar) × (50 L - 1 L)

= (-2) × 49 L

= -98 L bar

We know that 1 KJ bar = 101 J, So,

= -98 × 101 J

= -9999 J

= -9.999 KJ

In the first case, as the expansion is against constant external pressure, thus, the work done is negative which is low.

If the same expansion carried out reversibly, the internal pressure of gas is infinitesimally larger than the external pressure. Therefore, the final work done will be considered high.