Question

Calculate the average and total kinetic energy of $0.5mole$ of an ideal gas at $0^{\circ }C$.

Answer 1

Average kinetic energy per molecule of the gas
$=\frac{3}{2}\frac{R}{N}T$
$=\frac{3}{2}\times \frac{8.314\times {10}^7}{6.023\times {10}^{23}}\times 273$
$=5.65\times {10}^{-14}erg=5.65\times {10}^{-21}J$
Total kinetic energy of $0.5mole$ of the gas
$=\frac{3}{2}RT\times 0.5$
$=\frac{3}{2}\times 8.314\times {10}^7\times 273\times 0.5$
$=1.702\times {10}^{10}erg=1.720kJ$.