Question

The translational kinetic energy of the molecules of a gas at absolute temperature (T) can be doubled by

• A. increasing T to 4 T
• B. increasing T to \(\sqrt{2}\) T
• C. decreasing T to T/2
• D. increasing T to 2T

Hint:

Average translational energy is (3/2) kT, directly proportional to T.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
The average translational kinetic energy per molecule is \(\dfrac32k_BT\). It is directly proportional to the absolute temperature.

Step 2: Detailed Explanation:
To double the energy, the absolute temperature must double: \(T \to 2T\).
Raising \(T\) to \(4T\) would give four times the energy. Raising to \(\sqrt2\,T\) gives only \(\sqrt2\) times the energy. Decreasing to \(T/2\) halves the energy.

Step 3: Final Answer:
Option (D), increasing \(T\) to \(2T\).

Final Answer:
Kinetic energy is proportional to T, so double T. \[ \boxed{\text{(D) }T\to2T} \]