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 $4 \,kg/m^{3}$. What is the energy of the gas due to its thermal motion?

• A. $3 × 10^4\, J$
• B. $6 × 10^4\, J$
• C. $5 × 10^4\, J$
• D. $7 × 10^4\, J$

Answer 1

Answer: (C)

Thermal energy corresponds to internal energy
Mass $= 1 kg$
density $= 8 kg/m^3$
$\Rightarrow Volume=\frac{mass}{density}=\frac{1}{8}m^{3}$
Pressure $= 8 × 10^{4}\, N/m^{2}$
$\therefore $ Internal Energy $=\frac{5}{2}P × V = 5 × 10^{4}\, J$