Question

A vessel contains helium, which expands at constant pressure when $15kJ$ of heat is supplied to it. What will be the variation of the internal energy of the gas? (in $kJ$)

Answer 1

The first law of thermodynamics gives us the relation:
$q=\Delta U+w$
For constant pressure process,
$q=n{C}_p\Delta T$
$\Delta U=n{C}_v\Delta T$
$\frac{\Delta U}{q}=\frac{C_v}{C_p}=\frac{1}{\gamma }$
Helium is a monoatomic gas i.e $\gamma =\frac{5}{3}$
$\Delta U=\frac{1}{\gamma }q=\frac{3}{5}\times 15kJ=9kJ$