Question

One kg of a diatomic gas is at a pressure of 8 × 10⁴ N/m². The density of the gas is 4 kg/m³. What is the energy of the gas due to its thermal motion ?

• A. 3 × 10⁴ J
• B. 5 × 10⁴ J
• C. 6 × 10⁴ J
• D. 7 × 10⁴ J

Answer 1

Answer: (B)

5 × 10⁴ J

Answer 2

E = $\frac{f}{2}$RTn**.**

Since gas is diatomic hence f = 5

E = $\frac{5}{2}$ RTn ($\because$PV = nRT)

E = $\frac{5}{2}$PV

E = $\frac { 5 } { 2 }$ $\frac{PM}{D}\left( \begin{aligned} & M = Mass \\ & D = Density \end{aligned} \right)$E = $\frac{5}{2}$ × $\frac{8 \times 10^{4} \times 1}{4}$ = 5 × 10⁴ J.

So option (2 ) is correct.