IIT-JEE 2007 Assertion-Reason Type MCQ on Kinetic Energy of Gas Molecules

Assertion-Reason Type Multiple Choice Questions are often interesting to answer, as is the case with the following one which appeared in IIT-JEE 2007 question paper:

STATEMENT-1

The total translational kinetic energy of all the molecules of a given mass of an ideal gas is 1.5 times the product of its pressure and volume

because

STATEMENT-2

The molecules of a gas collide with each other and the velocities of the molecules change due to the collision

(A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.

(B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1.

(C) Statement-1 is True, Statement-2 is False

(D) Statement-1 is False, Statement-2 is True

Statement-1 is true. To prove this you may use the expression for the translational kinetic energy (E) of a gas molecule, given by

E = (3/2) kT

where ‘k’ is Boltzman’s constant and ‘T’ is the absolute (Kelvin) temperature.

[Remember that the translational kinetic energy of any type of molecule is (3/2)kT since the energy per degree of freedom is ½ kT and in our three dimensional space, there can be three translational degrees of freedom only]

The total translational kinetic energy of all the molecules of the given mass of gas is (3/2) kT×nV where ‘V’ is the volume of the gas and ‘n’ is the number of molecules per unit volume.

But, the pressure (P) of the gas is given by

P = nkT .

Therefore, total translational kinetic energy = (3/2)PV = 1.5 PV.

Statement -2 is true. In fact this follows from the postulates of kinetic theory. But, the pressure exerted by a gas is not because of the collision between the gas molecules, but is because of the collision of gas molecules with the walls of the container. So, statement-2 is not a correct explanation for statement-1.

The correct option therefore is (B).