Ideal Gas Pressure and Temperature – Rankers Physics
Topic: Thermal Physics
Subtopic: Kinetic Theory of Gases

Ideal Gas Pressure and Temperature

Assertion (A): When an ideal gas is heated in a rigid non conducting container then pressure becomes double if the temperature is doubled.
Reason (R): Both the frequency of collisions and momentum transferred per collision becomes \( \sqrt{2} \) times.
 
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:

Assertion (A) is true by ideal gas law \( P \propto T \) at constant volume. Reason (R) is also true, as \( v_{rms} \propto \sqrt{T} \), affecting both collision frequency and momentum transfer per collision by a factor of \( \sqrt{2} \) when T is doubled. (R) correctly explains (A).

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