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