Question

According to Kinetic theory of gases.
A) The velocity of molecules decreases for each collision.
B) The pressure exerted by the diatomic gas is proportional to the mean velocity of molecule
C) The K.E of the gas decreases on expansion at constant temperature
D) The mean translational KE of diatomic gas increases with increase in absolute temperature.

Answer 1

Hint: In a gas, the average intermolecular separation is much greater than that of solids and liquids. Gas molecules are very loosely confined to each other. Molecules of a gas are point masses and are identical for the same gas. The total energy of molecules remains constant during collisions. The molecular collisions are perfectly elastic and the molecules move with constant velocity along a straight line during two collisions.

Complete step by step answer:
In Kinetic theory of gases, molecules of each gas are identical but different from that of other gases. There are many postulates derived for Kinetic theory of gases.
One of the postulates is that the molecules are rigid and perfectly elastic spheres. This means that momentum and Kinetic energy are conserved. The momentum is conserved that means the velocity does not change after the collision.
Since, momentum = \[m\upsilon \]
where ‘m’ and ‘\[\upsilon \]’ are mass and velocities of the molecules respectively.
Thus, option (A) is not correct, as the velocity remains the same for each collision.
Pressure exerted on the walls of the container by the molecules is given by
\[p = \dfrac{1}{3}\rho C_{rms}^2\]
where, \[\rho \]is the density of the gas.
From the formula, the pressure is directly proportional to the root mean square velocity of the molecule. Thus, option (B) is also not correct.
If the temperature is kept constant under expansion, then the velocity of molecules will not change. Therefore, the KE will not change. Thus, option (C) is also not correct.
The mean Kinetic Energy of the molecule of an ideal gas is
\[U = \dfrac{3}{2}{k_b}T\]
where \[{k_b}\]is Boltzmann’s constant and T is the temperature.
From the formula, the KE is directly proportional to temperature. KE increases as the temperature increases.

So, the correct answer is “Option D”.

Note:
The Kinetic theory of gases is applicable for ideal gases and not for real gases. In this theory of ideal gases, the factors like the intermolecular forces and gravitational attraction are neglected.
The momentum and Kinetic energy are conserved, provided physical conditions such as pressure and temperature do not change. Increasing the temperature will increase the velocity of molecules and thus the momentum will increase.