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 $R=8.0Jmo{l}^{-1}{K}^{-1}$ , then how much is the decrease in its internal energy (in $J$ ) ?

Answer 1

Answer: 900

$V_i=V$
$V_f=8V$
For adiabatic process $\{\gamma =5/3$ for monoatomic gas $\}$
$T_1\cdot V_1^{\gamma -1}=T_2\cdot V_2^{\gamma -1}$
$100{\left(V\right)}^{\frac{2}{3}}=T_2{\left(8V\right)}^{\frac{2}{3}}$
$T_2=25K$
Loss in internal energy $\Delta U=n{C}_v\Delta T=1\left(\frac{fR}{2}\right)\left[100-25\right]=12\times 75=900J$