Question

A mixture of two gases consists of $3$ moles of nitrogen and $6$ moles of neon at temperature $27^{\circ }C$. Neglecting all vibrational modes, the total internal energy of the system is _________$\times 10^{4}J$.
$\left(R=8.32Jmo{l}^{-1}{K}^{-1}\right)$

Answer 1

Answer: 4.12

Internal energy of a gas with $f$ degrees of freedom,
$U=\frac{f}{2}nRT$
Now, $f_{N_2}=\frac{5}{2},f_{Ne}=\frac{3}{2}$
$\therefore U_{\text{total }}=U_{N_2}+U_{Ne}$
$=\frac{5}{2}\times 3\times 8.32\times (27+273)$
$+\frac{3}{2}\times 6\times 8.32\times (27+273)$
$=3\times 8.32\times 300\times \left(\frac{5}{2}+3\right)$
$=4.16\times 900\times 11$
$=41184J$
$\therefore U_{\text{total }}=4.12\times 10^{4}J$