question_answer 32)

                  The initial state of a certain gas is \[({{P}_{i}},\,{{V}_{i}},\,{{T}_{i}})\]. It undergoes expansion till its volume becomes \[{{V}_{f}}\]. 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:

                  (a) \[PV=RT\]                 If T is constant, \[PV=\] constant or \[\text{P=}\,\frac{\text{Constant}}{\text{v}}\]. The graph between P and V is shown by curve (a).                 (b) If P is constant, then graph between P and V is shown by the curve (b).                 Works done = area under P ? V diagram.                 Hence, more work will be done if then expansion takes place at constant pressure.