Question

According to kinetic theory of gases, which of the following statements are true

• A. Pressure of the gas molecule is proportional to most probable velocity of the gas molecules.
• B. The pressure exerted by the gas molecule is proportional to root mean square velocity of the gas molecules.
• C. The root mean square velocity is directly proportional to square root of the Kelvin temperature.
• D. Kinetic energy of the gas molecule does not depend upon, P, V and molar mass of the gas molecules.

Answer 1

Answer: (C), (D)

The correct options are
C The root mean square velocity is directly proportional to square root of the Kelvin temperature.
D Kinetic energy of the gas molecule does not depend upon, P, V and molar mass of the gas molecules.

(a) The pressure of gas is given as:
$PV=\frac{1}{3}mN{C}^2$
where C =velocity of gas (in this case most probable velocity)
So pressure is directly propotional to square of velocity.
(b) $PV=\frac{1}{3}mN{C}^2$
here C = root mean square velocity
So pressure is directly propotional to square of root mean square velocity.
(c) $C=\sqrt{\frac{3RT}{M}}$
So the root mean square velocity is directly proportional to square root of the absolute temperature.
(d) $KE=\frac{3}{2}RT$
Kinetic energy of gas molecule depends only on absolute temperature.