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Question

The pressure exerted by 6×1023 chlorine molecules, n of which will strike per second on a wall of area A at an angle 60 with the normal, if the mass of Cl2 molecules is m and speed of each Cl2 molecule is v, is given by :
  1. 2mvnA
  2. mnvA
  3. mvnA
  4. 2mnvA


Solution

The correct option is B mnvA
Momentum of each chlorine molecule with which it strikes the wall normally
=mvcosθ
Each molecule rebounds with the same momentum.
So, the change of momentum
=mvcosθ(mvcosθ)
=2mvcosθ
If n molecules strike per second on the wall, then change in momentum per second, i.e., force =2mvcosθ×n and force per unit area
=FA=2mnvcosθA
Thus, pressure exerted on the wall is
P=2mnvcosθA=2mnvcos60A=mnvA

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