Exam

JEE Main

Year

2015

Date

10 April

Mode

Online

Subject

Physics

Chapter

Kinetic Theory of Gases

JEE Main 2015 · 10 April · Online · Physics · Kinetic Theory of Gases

In an ideal gas at temperature T, the average force that a molecule...

In an ideal gas at temperature T, the average force that a molecule applies on the walls of a closed container depends on $Tas{T}^{q}$ . A good estimate for q is:

Step-by-step solution

Average linear velocity for collision to occur

$t = \dfrac{2d}{u}$

Change in momentum in 1 collision

$\Deltap = 2mu$

$∴$ average force in collision

$= \dfrac{\Deltap}{t}$

($u =$ root mean square speed)

$= \dfrac{2mu}{2d} \times u$

$⇒ F ∝ {u}^{2}$

$∴ {u}^{2} ∝ T$

$⇒ F ∝ T$

$⇒ q = 1$