Question

Calculate the work done by a gas as it is taken from the state a to b, b to c and c to a as shown in figure.

• A. 40 J
• B. -40 J
• C. -10 J
• D. 10 J

Answer 1

The correct option is D

10 J

Let us calculate the work done for each individual process.

Process a - b
The work done is equal to the area of rectangle acdb
$=120\times {10}^3\times 250\times {10}^6$

= 30 J.
Process b - c
Since there is no change in volume,dV is equal to zero. Hence the work done $(W=\int PdV)$ is also equal to zero.
Process C - a
The work done in this process

= area of rectangle acdb + area of $\Delta abc$

$=(30+\left(\frac{1}{2}\right)80\times {10}^5\times 250\times {10}^6)J$

= (30 + 10)J= 40 J.

However the work done is -40 J since the process reduces the volume of the gas.
Hence total work done is
= work done in (a - b) + work done in (b - c) + work done in (c - a)

= (30 + 0 - 40) J

= -10 J.