(a) From first law of thermodynamics,
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ Q = \mathrm{\Delta}U + W$
For path iaf,
$50 = \mathrm{\Delta}U + 20$
$\therefore\ \ \ \ \ \ \ \mathrm{\Delta}U = U_{f} - U_{i} = 30\ cal$
For path ibf,
$Q = \mathrm{\Delta}U + W$
or $W = Q - \mathrm{\Delta}U$
=36-30=6cal