Kinetic Energy of Ideal Gas – Rankers Physics

Kinetic Theory of Gases: Practice Problem & Solution

Assertion (A): 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. Reason (R): The molecules of a gas collide with each other and the velocities of the molecules change due to the collision.  
Both (A) & (R) are true and the (R) is the correct explanation of the (A)
Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
(A) is true but (R) is false
Both (A) and (R) are false

Solution Explained:

To solve this problem, we apply the core principles of Kinetic Theory of Gases. Understanding the underlying formula is key to arriving at the correct answer below:

Assertion (A) is true because \( E_k = \frac{3}{2} nRT \) and \( PV = nRT \), so \( E_k = \frac{3}{2} PV \). Reason (R) is also true, as molecules of an ideal gas undergo elastic collisions with each other, changing their individual velocities. However, (R) does not explain (A).

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