Question

A perfect gas of 'N' molecules, each of mass 'm', moving with velocities 'C₁', 'C₂', ...... .'C_N' is enclosed in a cubical vessel of volume 'V'. The pressure exerted by the gas on the walls of the vessel is ______. ('p' = density of gas)

Options

• `1/3 "mN"/"V" "C"_"RMS"`

• `1/3 "m"/"V" "C"_"RMS"^2`

• `1/3 rhobar"C"^2`

• `1/2 rhobar"C"^2`

Answer 1

A perfect gas of 'N' molecules, each of mass 'm', moving with velocities 'C₁', 'C₂', ...... .'C_N' is enclosed in a cubical vessel of volume 'V'. The pressure exerted by the gas on the walls of the vessel is `underline(1/3 rhobar"C"^2)`.

Explanation:

P = `1/3 rho "C"_"RMS"^2`

Now, `"C"_"RMS" = sqrt(bar"c"^2)`