Question

One mole of an ideal monoatomic gas is initially at $300K$. Find the final temperature (in $K$) if $200J$ of heat is added at constant pressure.

Answer 1

Heat supplied to a system is given by:$\delta q=\int nCdT$

where $n$ is the number of moles of the gas and $C$ is the specific heat capacity for the process.
Here it is given that the process is a constant pressure process.
Thus $C=C_p$
so we get $\Delta T=\frac{q}{n{C}_p}$
For a monoatomic ideal gas. $C_p=\frac{\gamma R}{\gamma -1}$ where $\gamma =\frac{5}{3}$
$⟹C_p=\frac{5}{2}R$

Given : $q=200J$, $T_1=300K$ and $n=1$
$\Delta T=\frac{2q}{5nR}=\frac{2\times 200}{5\times 1\times 8.314}=10K$
i.e. $\Delta T=T_2-T_1=10K$
$⟹T_2=T_1+10=300+10=310K$