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Unformatted text preview: the time dt . The pressure, P , exerted on the wall is the force per unit area as follows V N E V N mv v mv dt dp A A F P A A 4 ) 2 ( ) )( 2 ( 1 2 = = = = = where 2 2 1 mv E = is the kinetic energy of the particles. Thus, E N V P A 4 = . However, the actual motion is random so the true pressure P of each face of the cube is P /6 ( six directions ) and hence E N PV A 3 2 = , where <E> is the average kinetic energy of the particles. Boltzmanns Constant: Absolute temperature, T , is defined so that kT kT kT kT E 2 1 2 1 2 1 2 3 + + = = where K J k / 10 38 . 1 23 = . Thus, for n moles we get, nRT PV = with k N R A = . Random Motion vdt Wall with area A Ideal Gas Law Universal Gas Constant Boltzmanns constant converts from temperature to energy! (although they are not the same thing) 3 degrees of freedom...
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 Spring '07
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 Physics, Energy

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