Let vₐᵥ, vᵣₘₛ and vₚ denote the mean speed, root-mean-square speed and most probable speed, respectively, of molecules of an ideal monoatomic gas at absolute temperature T. If the molecular mass is m, then:
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Question

Let vₐᵥ, vᵣₘₛ and vₚ denote the mean speed, root-mean-square speed and most probable speed, respectively, of molecules of an ideal monoatomic gas at absolute temperature T. If the molecular mass is m, then:

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G1 Physics · Accepted Answer

Use PV=nRT, U=(f/2)nRT, γ=1+2/f and vᵣₘₛ=√(3RT/M). At the same temperature, average translational kinetic energy depends only on T. Evaluating the given data/statements gives C: vₚ<vₐᵥ<vᵣₘₛ; D: Average kinetic energy is (3/4)mvₚ². Therefore the correct answer is C, D.