Question

$3.2\, m ^{3}$ of a gas is heated at the pressure $10^{5} \,N / m ^{2}$ until its volume increases by $25 \%$. Then, the external work done by the gas is ________$\times 10^{4} J$.

Answer 1

External work done $= PdV = P \left( V _{2}- V _{1}\right)$
$V _{1}= V =3.2 m ^{3}$ and
$V _{2} = V +25 \% V $
$= V +\frac{25 V }{100} $
$= V +0.25 \,V $
$\therefore W = P ( V +0.25 V - V ) $
$=0.25 \,PV$
$=0.25 \times 10^{5} \times 3.2 $
$=0.8 \times 10^{5} $
$\therefore W =8 \times 10^{4} J$