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 its volume.
because
STATEMENT-2
The molecules of a gas collide with each other and the velocities of the molecules change due to the collision.
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 its 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✓ Correct
- (C)Statement-1 is True, Statement-2 is False
- (D)Statement-1 is False, Statement-2 is True
Answer: (B)
Solution
Statement-1 is TRUE: From kinetic theory, the total translational kinetic energy of an ideal gas is:
(using ideal gas law )
So the total translational KE is indeed 1.5 times .
Statement-2 is TRUE: Molecules in a gas do collide with each other, and these collisions change individual molecular velocities. This is a fundamental aspect of kinetic theory.
However, Statement-2 is NOT a correct explanation for Statement-1. The relationship comes from the ideal gas law and the equipartition theorem, not from the fact that molecules collide. The collisions ensure thermal equilibrium and the Maxwell-Boltzmann distribution, but the 1.5 factor is a consequence of the three translational degrees of freedom.
Therefore, the answer is (B).
(using ideal gas law )
So the total translational KE is indeed 1.5 times .
Statement-2 is TRUE: Molecules in a gas do collide with each other, and these collisions change individual molecular velocities. This is a fundamental aspect of kinetic theory.
However, Statement-2 is NOT a correct explanation for Statement-1. The relationship comes from the ideal gas law and the equipartition theorem, not from the fact that molecules collide. The collisions ensure thermal equilibrium and the Maxwell-Boltzmann distribution, but the 1.5 factor is a consequence of the three translational degrees of freedom.
Therefore, the answer is (B).
JEE Advanced · 2007 · 08 Apr 2007 · Paper 2 · Single correct option