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Derive the relation between pressure and mean kinetic energy. |
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Answer» Solution :The internal of the gas is given by `U = 3/2 NkT` The above equation can ALSO be a written as `U=3/2 PV` Since , PV = NkT `P = 2/3 U/V = 2/3 u "" …(1)` From the equation (1), we can state that the pressure of the gas is equal to two thirds of internal energy per unit VOLUME or internal energy DENSITY `(u = U/V)` . Writing pressure in terms of mean kinetic energy density using equation, `P =1/3nmbar(v^2) =1/3rhobar(v^2)"" ...(2)` where `rho` = nm = mass density (Note n is number density) Multiply and divide R.H.S of equation (2) by 2 , we get `P = 2/3 (rho/2bar(v^2))` `P = 2/3 bar(KE)` |
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