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 $4Kg/m^3$. The energy of the gas due to its thermal motion is

• 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 $5\times {10}^{4}J$

Thermal energy corresponds to internal energy,
mass = 1kg
density = $8kg/m^3$
$\therefore$ volume (v) = $\frac{mass}{density}=\frac{1}{8}{m}^3$
Pressure (p) = $8\times {10}^{4}N/m^3$
$\therefore$ Internal energy = $\frac{5}{2}\left(PV\right)=5\times {10}^{4}J$.