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Q.

In a cubical vessel are enclosed n molecules of a gas each having a mass m and an average speed v . If l is the length of each edge of the cube, the pressure exerted by the gas will be

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a

nmv2ℓ3

b

nm2v2ℓ3

c

mnv23ℓ3

d

nmv2ℓ

answer is C.

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Detailed Solution

Change in momentum will be Δp=2mvxTime of collision between two walls=Δt=2 ℓvxForce by all molecules acting on wall=F=ΔpΔt=nmvx2ℓDue to randomness in all three directions,vx2=v23∴F=mnv23ℓSo, presssure on wall=FA=mnv23ℓ3
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