Carbon dioxide ( ) is drawn into a kiln at and leaves in the flue at

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

Carbon dioxide (

M = 44.01\ \mathrm{g\,mol^{-1}}

) is drawn into a kiln at

20.0\ ^\circ\mathrm{C}

and leaves in the flue at

500\ ^\circ\mathrm{C}

. Treat it as a dilute ideal gas in equilibrium at each temperature. A classmate says: "the temperature has gone up by a factor

500/20 = 25

, so the rms speed has gone up by

\sqrt{25} = 5.0

." ((a)) Find

v_{\rm rms}

of the carbon dioxide at each of the two temperatures. ((b)) Find the true factor by which

v_{\rm rms}

increases, and say in one sentence what is wrong with the classmate's step. ((c)) Find

v_p

and

\bar v

in the flue, and state whether the ratios

v_p : \bar v : v_{\rm rms}

have changed on heating. Use

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

and

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

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