Q. One kg of a diatomic gas is at a pressure of $8 \times 10^{4}\ Nm^{- 2}$. The density of the gas is $4\ kgm^{- 3}$. What is the energy of the gas due to its thermal motion?
A) $3 \times 10^{4}\ J$
B) $5 \times 10^{4}\ J$
C) $6 \times 10^{4}\ J$
D) $7 \times 10^{4}\ J$
Explanation
(b) Thermal energy corresponds to internal energy
Mass=1 kg
Density = 4 $kg\ m^{- 3}$
Volume = $\frac{Mass}{Density} = \frac{1}{4}\ m^{3}$
Pressure = $8 \times 10^{4}\ Nm^{- 2}$
$\therefore\ \ \ \ \ \ \ \ \ \ \ Internal\ energy = \frac{5}{2}\ p \times V = 5 \times 10^{4}\ J$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.