A sealed rigid flask holds of methane

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 sealed rigid flask holds

0.50\,\mathrm{mol}

of methane, molar mass

M = 16.0\,\mathrm{g\,mol^{-1}}

, at

300\,\mathrm{K}

. The methane molecule is not linear, so it has three rotational quadratic degrees of freedom as well as its three translations; its vibrations may be taken as inactive at this temperature. Treat the gas as dilute and ideal and take equipartition of energy to hold for the active degrees of freedom. ((a)) Find the root-mean-square speed of a methane molecule at

300\,\mathrm{K}

. ((b)) Find the energy that must be delivered to the flask's contents at fixed volume to raise their temperature by

20\,\mathrm{K}

. Use

k_B = 1.381\times10^{-23}\,\mathrm{J\,K^{-1}}

N_A = 6.022\times10^{23}\,\mathrm{mol^{-1}}

and

R = 8.314\,\mathrm{J\,K^{-1}\,mol^{-1}}

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