Calculate the thermal conductivity of He at 1 atm and 0ºC and at 10 atm and 100ºC. Use the value of the molecular diameter obtained from viscosity measurements at 1 atm and 0ºC, d=2.2 Anstrong. The experimental value at 0°C and 1 atm is $1.4x10^{-3}$ J/Kcms.
Solution:
We will use the more exact equation: \begin{equation} k=\frac{25}{32}\left(\frac{RT}{\pi M}\right)^{1/2}\frac{1}{N_Ad ^2}C_{vm} \end{equation} We make the substitutions: $N_A=6.022x10^{23}\;1/mol$; T=273K; $d=2.2x10^{-10}\;m$; $C_{vm}=3/2R$ with R=8.314 J/molK; $M=4x10^{-3}Kg/mol$
The result is k=0.142 J/Kms