Question

One Kg of a diatomic gas is at a pressure of $8\times {10}^4$N/ $m^2$. The density of the gas is $4$kg/ $m^3$. The energy of the gas due to its thermal motion will be

• A. $3\times {10}^4$J
• B. $5\times {10}^4$J
• C. $6\times {10}^4$J
• D. $7\times {10}^4$J

Answer 1

The correct option is B $5\times {10}^4$J

For a diatomic molecular gas, internal energy per molecule is
$U=\frac{5}{2}N{K}_{B}T$
$PV=N{K}_{B}T$
From equation is (i) and (ii)
$U=\frac{5}{2}$PV
Here, $P=8\times {10}^{4}N$ $m^{-2},\rho =4kg$ $m^{-3}$, $m=1$kg
$\therefore U=\frac{5}{2}\times 8\times {10}^4\times \frac{1}{4}=5\times {10}^4$J