Question

Kinetic energy and pressure of a gas of unit volume are related as:

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

Answer 1

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

By ideal gas equation,
$PV=RT$
Given,
$V=1$
$P=RT$...(i)
By kinetic molecular theory of gases:
$E=\frac{3}{2}RT$...(ii)
By (i) and (ii)
$E=\frac{3}{2}P$
Rearranging we get
$P=\frac{2}{3}E$