Question

The diagram shows a $P-V$ graph of a thermodynamic behaviour of an ideal gas. Find out from this graph (i) work done in the process $A\to B,B\to C,C\to D$ and $D\to A$, (ii) work done in the complete cycle $A\to B\to C\to D\to A$

Answer 1

(i) Work done in the process $A\to B$ (the process is expansion, hence work done by the gas)
$=-P\times dV=-12\times {10}^5\times 5\times {10}^{-3}$
$=-6000J$
Work done in the process $B\to C$ is zero as volume remains constant.
Work done in the process $C\to D$ (the process is contraction hence work done on the gas)
$=P\times dV=2\times {10}^5\times 6\times {10}^{-3}$
$=1000J$
(ii) Work done in the process $D\to A$ is zero as volume remains constant.
Net work done in the whole cycle $=-6000+1000=-5000J$
i.e., net work is done by the gas.