In a cubical box of volume V, there are N molecules of a gas moving randomly. If m is mass of each molecule and v2 is the mean square of x component of the velocity of molecules, then the pressure of the gas is
A
P=13mNv2V
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B
P=mNv2V
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C
P=13mNv2
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D
P=mNv2
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Solution
The correct option is BP=mNv2V Let the mass of each molecule be m. ∴ Pressure P=13ρv2rms =13mNV.v2rms.....(1)
Root mean square velocity is v2rms=v2x+v2y+v22 vx=vy=vz=v v2rms=3v2 ∴ From equation (1). P=13mNV.3v2 P=mNv2V