InterviewSolution
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InterviewSolution
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Calculate the average kinetic energy for one molecule of gas at constant volume. |
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Answer» Pressure exerted by one mole of gas, \(P=\frac{1}{3}ρv^2_{rms}\) \(=\frac{1}{3}\frac{M}{V}v^2_{rms}\) or, \(PV=\frac{1}{3}Mv^2_{rms}\) But PV = RT ∴ \(\frac{1}{3}Mv^2_{rms}\) = RT \(Mv^2_{rms}\) = 3RT Now, average KE \(\frac{1}{3}Mv^2_{rms}\) = \(\frac{3}{2}\)RT \(\frac{1}{2}(Nm)v^2\) = \(\frac{3}{2}\)RT (∵ M = Nm) (KE)Avg for one mole \(\frac{1}{3}Mv^2_{rms}\) = \(\frac{3}{2}\frac{R}{N}T\)= \(\frac{3}{2}\)kBT ∴ Total random K.E. for one mole =\(\frac{3}{2}\)RT and average K.E. per molecule = \(\frac{3}{2}\)kBT |
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