Question

Kinetic energy and pressure of a gas of unit mole are related as

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

Answer 1

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

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

$PV=\frac{1}{3}mN{u}^2$.....(1)

$K.E=\frac{1}{2}mN{u}^2$.....(2)

Divide (2) with (1)
$\frac{K.E}{PV}=\frac{\frac{1}{2}mN{u}^2}{\frac{1}{3}mN{u}^2}$

$\frac{K.E}{PV}=\frac{3}{2}$

$PV=\frac{2}{3}K.E$