Question

Which of the following relations is correct for an ideal gas regarding its pressure (P) and translational kinetic energy per unit volume (E)?

• A. $P=\frac{2}{3}E$
• B. $P=\frac{3}{2}E$
• C. $P=\frac{1}{2}E$
• D. $P=2E$

Answer 1

The correct option is A $P=\frac{2}{3}E$

According to kinetic theory of gases,
$E=\frac{1}{2}m{u}_{rms}^2=\frac{1}{2}mN{u}_{rms}^2$
Energy per unit volume $E=\frac{E}{V}=\frac{1}{2}\frac{mN{u}_{rms}^2}{V}$
$=\frac{3}{2}\times \frac{1}{3}\frac{mN{U}_{rms}^2}{V}=\frac{3}{2}P(asPV=\frac{1}{3}mN{u}_{rms}^2)$
So $P=2/3E$