Question

The indicator diagrams representing maximum and minimum amounts of work done are respectively

A) a and b
B) b and c
C) b and d
D) c and d

Answer 1

Hint: The work done when a gas is compressed or expands is basically given by the area under the curve in a PV diagram. If the work done is carried out in such a way that the net volume reduces, the work done is negative and if it increases the work done is positive. Hence by determining the area under the curve of pressure and change in volume, will enable us to determine the graph of maximum and the minimum work done.

Formula used:
$W=\int{PdV}$

Complete step-by-step answer:
Let us say if a gas is compressed or it expands, the work done (W) at pressure P such that the change in volume is ‘dV’ is given by,
$W=\int{PdV}$
From the above equation we can draw a conclusion if the volume of the gas does not change in a PV diagram i.e. ‘dV = 0’, we can imply the work done will be zero or minimum. In graph d, the volume of the gas does not change. Hence the minimum work done corresponds to graph ‘d’.
The above equation of work done basically means the area under the PV curve in the PV diagram. If we observe the above graphs, The coordinate of pressure in graph b is the highest whereas the change in volume for all of them is approximately the same. Since work done is the product of pressure times the change in volume the area under the graph of ‘b’ is maximum and hence the work done is also maximum.

So, the correct answer is “Option C”.

Note: It is to be noted that the net work done in graph ‘a’ is negative. This does not mean that the work done is smaller. The basic interpretation of that is that the work is done on the gas and not by the gas.