Question 160 of 168

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:

A$2$B$\dfrac{1}{2}$C$1$D$\dfrac{1}{4}$

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Answer: (C) $1$

Average linear velocity for collision to occur

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

Change in momentum in 1 collision

$\Delta p=2mu$

$∴$ average force in collision

$=\dfrac{\Delta p}{t}$

($u=$ root mean square speed)

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

$\Rightarrow F\propto {u}^{2}$

$∴{u}^{2}\propto T$

$\Rightarrow F\propto T$

$\Rightarrow q=1$

JEE Main Physics practice question on Kinetic Theory (Pressure and Energy of gas), with the answer and a step-by-step solution. Scan a question from your own book or paper to get a whiteboard video.