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Question

# A vessel contains 6×1029 molecules of a gas per cubic metre. The mass of each molecule is 5×10−27 kg. If the molecules are moving with velocity 1 Km sec−1.What is the pressure of the gas?

A
103 Pa
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B
105 Pa
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C
107 Pa
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D
109 Pa
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Solution

## The correct option is B 109 PaApplying formula, PV=1/3mNv2or, P=1/3m(N/V)v2where P is pressurem is mass of molecule.(N/V) is number of molecules per unit volume.v is velocity of molecule.m = 5×10−27 Kg,N/V=6×1029/m3v=1km/sec=1000m/snow, Pressure, P=1/3×5×10−27kg×(6×1029/m3)×(1000m/s)2=5×102×2×106Kg/m/s2=10×108N/m2=109N/m2Hence, the pressure of a gas in the vessel is 109 Pa.

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