Question

Figure shows the variation of internal energy "U" with the density ${}^{\prime \prime }\rho {}^{\prime \prime }$ of one mole of ideal diatomic gas. Process BA is a part of rectangular hyperbola. If the work done by gas in the process $B\to A$ is W joules. Find W ?

Answer 1

For rectangular hyperbola
XY = constant
$U\rho =constant$
$n{C}_{V}T\rho =constant$
$n\frac{5}{2}RT\frac{M}{V}=constant$
$\frac{5}{2}P\frac{VM}{V}=constant$
$\Rightarrow$ P = constant (isobaric process)
$\Delta U_{B\to A}=7-2=5J=\frac{5}{2}nR\Delta T$
$2J=nR\Delta T$
$\therefore W=P△V=nR△T=2J$