Chapter3_3 - the time dt The pressure P exerted on the wall...

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PHY3063 R. D. Field Department of Physics Chapter3_3.doc University of Florida Temperature and Boltzmann’s Constant What is temperature? As the temperature increases the average kinetic energy associated with the random motion of the constituents ( i.e. atoms or molecules) of the macroscopic body increases. At 0 o K all random motion stops. Note that T K = T C + 273.15 and T F = 9T C /5 + 32 , where T K , T C , and T F correspond Kelvin (absolute) , Centigrade , and Fahrenheit temperature scales. Kinetic Theory of Ideal Gasses: Consider a volume V containing one mole of identical particles with mass m . Suppose that all the particles are moving to the right at speed v . Each particle transfers momentum 2mv to the wall. The density of particles is ρ = N A /V . The amount of momentum transferred to the area A in a time dt is given by dp = (2mv)N , where N = ρ (vdt)A is the number of particles hitting the wall in
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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 = = = = = ρ 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. Boltzmann’s 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 Boltzmann’s constant converts from temperature to energy! (although they are not the same thing) 3 degrees of freedom...
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This note was uploaded on 05/29/2011 for the course PHY 3063 taught by Professor Field during the Spring '07 term at University of Florida.

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