Question

One mole of an ideal monoatomic gas is subjected to changes as shown in the graph. The magnitude of the work done (by the system or on the system) is _______ $J$ (nearest integer)

Given : $\log 2=0.3$
$\ln 10=2.3$

Answer 1

$ 1 \rightarrow 2 \Rightarrow $ Isobaric process
$ 2 \rightarrow 3 \Rightarrow $ Isochoric process
$ 3 \rightarrow 1 \Rightarrow $ Isothermal process
$W = W _{1 \rightarrow 2}+ W _{2 \rightarrow 3}+ W _{3 \rightarrow 1}$
$ =\left(- P \left( V _2- V _1\right)+0\left[- P _1 V _1 \ln \left(\frac{ V _2}{ V _1}\right)\right]\right) $
$ =\left[-1 \times(40-20)+0+\left[-1 \times 20 \ln \left(\frac{20}{40}\right)\right]\right] $
$ =-20+20 \ln 2$
$ =-20+20 \times 2.3 \times 0.3 $
$ =-6.2 \text { bar } L$
$| W |=6.2 \text { bar } 1=620\, J $