Question

The initial state of a certain gas is (P_i,V_i,T_i). It undergoes expansion till its volume becomes Vf Consider the following two cases:

(a) The expansion takes place at constant temperature.

(b) The expansion takes place at constant pressure.

Plot the P-V diagram for each case. In which of the two cases, is the work done by the gas more?

Answer 1

The P-V diagram for each case is shown in the figure.

(a) In case (i) P_iV_i = P_fV_f ; therefore process is isothermal. Work done = area under the PV curve.

(b) The expansion is at constant pressure P_i, so (ii) is isobaric process

Area enclosed by graph (i) is less than (ii), so work done is more when the gas expands to constant pressure (case ii).