Krypton (molar mass ) is a monatomic gas

PHYSICS · Multi-part · Fermi University Physics · Thermal, Statistical & Complex Systems · Statistical mechanics of ideal classical systems · Statistical mechanics of ideal classical systems

Thermal Physics, Ch The classical ideal gas from the partition function

Problem

Krypton (molar mass

83.80\,\mathrm{g\,mol^{-1}}

) is a monatomic gas. Treat it as an ideal gas of identical structureless atoms at

T = 298.15\,\mathrm{K}

and

p = 1.000\,\mathrm{bar} = 1.000\times10^{5}\,\mathrm{Pa}

, and use

\lambda_T = \frac{h}{\sqrt{2\pi mk_BT}}, \qquad S = Nk_B\left[\ln\!\left(\frac{1}{n\lambda_T^3}\right) + \frac52\right],

with

n = N/V

the number density. Take

h = 6.626\times10^{-34}\,\mathrm{J\,s}

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

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

and

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

. ((a)) Compute

\lambda_T

for krypton at this temperature. ((b)) Compute the number density and hence

n\lambda_T^3

; confirm that the classical condition holds. ((c)) Evaluate the molar entropy of krypton at these conditions. (The tabulated calorimetric value is

164.1\,\mathrm{J\,K^{-1}\,mol^{-1}}

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