A balloon is filled with helium

PHYSICS · Multi-part · Fermi University Physics · Thermal, Statistical & Complex Systems · Kinetic theory and transport in gases · Kinetic theory and transport in gases

Thermal Physics, Ch Temperature, pressure and the kinetic theory of gases

Problem

A balloon is filled with helium, a monatomic gas of molar mass M=4.00 g mol−1M = 4.00\,\mathrm{g\,mol^{-1}}, and sits in sunshine at T=350 KT = 350\,\mathrm{K}. Treat the helium as a dilute ideal gas and take equipartition of energy to hold, with only the three translational degrees of freedom of an atom active. ((a)) Find the root-mean-square speed of a helium atom at this temperature. ((b)) Find the energy that must be delivered per kelvin at fixed volume, per mole of this gas. Use kB=1.381×10−23 J K−1k_B = 1.381\times10^{-23}\,\mathrm{J\,K^{-1}}, NA=6.022×1023 mol−1N_A = 6.022\times10^{23}\,\mathrm{mol^{-1}} and R=8.314 J K−1 mol−1R = 8.314\,\mathrm{J\,K^{-1}\,mol^{-1}}.

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