Question

One mole of an ideal monatomic gas undergoes an adiabatic expansion in which its volume becomes eight times its initial value. If the initial temperature of the gas is $100K$ and the universal gas constant $R=8.0J \, mol^{- 1}K^{- 1}$ , then how much is the decrease in its internal energy (in $J$ ) ?

Answer 1

$V_{i}=V$
$V_{f}=8V$
For adiabatic process $\left\{\right.\gamma = 5/ 3$ for monoatomic gas $\left.\right\}$
$T_{1} \cdot V_{1}^{\gamma - 1} = T_{2} \cdot V_{2}^{\gamma - 1}$
$100\left(V\right)^{\frac{2}{3}}=T_{2}\left(8 V\right)^{\frac{2}{3}}$
$T_{2}=25 \, K$
Loss in internal energy $\Delta U=nC_{v}\Delta T=1\left(\frac{f R}{2}\right)\left[100 - 25\right]=12\times 75=900 \, J$