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What is the relation between the average kinetic energy and pressure? |
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Answer» Solution :The internal energyof the gas is GIVEN by ` U = 3/2NkT` The aboveequation can alsobe writtenas ` U = 3/2 PV` sincePV = NkT `P= 2/3 U/V= 2/3 u` From the equation (1),the pressure of the gas is equal to twothirds of internal ENERGYPER unitvolume or internal energy per unit volume or internal energydensity ( u = UV) Writingpressure in TERMS of meankineticenergy densityusing equation ` P = 1/3 nmv^(bar2) = 1/3 pv^(bar2)` Where p= nm = massdensity( Note n is number f density) Multiplyand divideR.H.S of equation (2) by 2,we get ` P = 2/3 ( P/2 bar(v^(2)))` ` P = 2/3 K E ` From the equation (3) , pressureis equalto 2/3of mean kineticenergyper unitvolume. |
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