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Question
Show that the average energy per molecule is proportional to the absolute temperature T of the gas.
Solution
The expression for the pressure exerted by a gas on the basis of kinetic theory of gas is given by
`P = 1/3(Nm)/v v_(rms)^2`
`PV=1/3xx2xx1/2xxNmv_(rms)^2`
`PV = 2/3E, ...(becauseE=1/2xxNmv_(rms)^2)`
By definition,
PV = RT ...(for one mole)
`RT = 2/3E`
`E=3/2RT`
`E=3/2Nk_BT ...(becauseR=Nk_B)`
`E/N=3/2k_BT`
`E/NmuT`
Average energy, per molecule, is directly proportional to absolute temperature T of the gas.
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