Question

Five moles of an ideal monoatomic gas with an initial temperature of ${127}^{0}C$ expand and in the process absorb 1200 J of heat and do 2100 J of work. What is the final temperature of the gas in ${}^{0}C$ ?

Answer 1

First law of thermodynamics gives us the relation:
$\delta q=\Delta U+w$
Given that
$\delta q=1200J$
$w=2100J$
this implies that $\Delta U=-900J$
also $\Delta U=n{C}_v\Delta T$
$C_v=\frac{3R}{2}$
i.e. $\Delta T=\frac{\Delta U}{n{C}_v}=\frac{2\Delta U}{3nR}=\frac{-2\times 900}{3\times 5\times 8.314}=-14K$
$\Delta T=T_2-T_1=-14K$ i.e. $T_2={113}^{\circ }C$