Question

A diatomic gas is heated at constant pressure. If $105J$ of heat is given to the gas, then the change in internal energy of the gas (in $J$) is

Answer 1

From First law of thermodynamics
$\Delta Q=\Delta U+\Delta W$
For isobaric process
$\Delta Q=\Delta U+nR\Delta T$
Relation between internal energy and degree of freedom is
$\Delta U=\frac{fnR\Delta T}{2}\Rightarrow nR\Delta T=\frac{2\Delta U}{f}$

$\Delta Q=\Delta U(1+\frac{2}{f})$

For a diatomic gas, $f=5$

$\Delta U=\Delta Q\frac{5}{7}=\left(105\right)\frac{5}{7}=75J$