Question

An ideal gas is taken through the cycle $ABCA$, as shown in the figure. What will be the work done by the gas in process CA (in J) if the net heat supplied to the gas in the cycle is $15\, J$ ?

Answer 1

For cyclic process,
Total work done $= W _{ AB }+ W _{ BC }+ W _{ CA }$
$\therefore \Delta W _{ AB }= P \Delta V =20(3-1.5)=30\, J$
and $ \Delta W _{ BC }=0$
From $1^{\text {st }}$ law of thermodynamics,
$ \Delta Q =\Delta U +\Delta W $
$ \Delta U =0 $ (Process $ ABCA$ is cyclic)
$ \therefore \Delta Q =\Delta W _{ AB }+\Delta W _{ BC }+\Delta W _{ CA } $
$\therefore 15=30+0+\Delta W _{ CA }$
$\therefore \Delta W _{ CA }=-15 \,J$