Question

Which of the following gases possesses the largest internal energy?

• A. $2$ moles of helium occupying $1{\text{m}}^3$ at $300\text{K}$
• B. $56\text{g}$ of nitrogen at ${10}^7{\text{Nm}}^{-2}$ and $300\text{K}$
• C. $8\text{g}$ of oxygen at $8\text{atm}$ and $300\text{K}$
• D. $6\times {10}^{26}$ molecules of argon occupying $40{\text{m}}^3$ at $900\text{K}$

Answer 1

The correct option is D $6\times {10}^{26}$ molecules of argon occupying $40{\text{m}}^3$ at $900\text{K}$

Helium is monoatomic
$\therefore U=2\times \frac{3}{2}R\times 300=900R$
Nitrogen is diatomic
$\therefore U=\frac{56}{28}\times \frac{5R}{2}\times 300=1500R$
Oxygen is diatomic
$U=\frac{8}{32}\times \frac{5R}{2}\times 300=187.5R$
Argon in monoatomic
$\therefore U=\frac{6\times {10}^{26}}{6\times {10}^{23}}\times \frac{3R}{2}\times 900=1.35\times {10}^{6}R$
So, $U$ is highest for $Ar$.
Hence, the correct option is D.