Chlorine 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

Chlorine gas (Cl2\mathrm{Cl_2}, molar mass 70.9 g mol−170.9\,\mathrm{g\,mol^{-1}}) is dilute enough to be treated as an ideal gas, so that translation, rotation and vibration are independent and their contributions to CVC_V add. Its characteristic temperatures are θrot=0.351 K\theta_{\rm rot} = 0.351\,\mathrm{K} and θvib=805 K\theta_{\rm vib} = 805\,\mathrm{K}. Electronic excitation and dissociation are ignored. Use the results of this chapter: translation contributes 32kB\tfrac32 k_B per molecule; rotation contributes kBk_B per molecule when T≫θrotT \gg \theta_{\rm rot} and nothing when T≪θrotT \ll \theta_{\rm rot}; and one vibrational ladder contributes CvibNkB=x2ex(ex−1)2,x=θvibT.\frac{C_{\rm vib}}{Nk_B} = \frac{x^2e^{x}}{(e^{x}-1)^2}, \qquad x = \frac{\theta_{\rm vib}}{T}. Take R=8.314 J K−1 mol−1R = 8.314\,\mathrm{J\,K^{-1}\,mol^{-1}}. ((a)) Predict CV/NkBC_V/Nk_B and the molar CVC_V at 300 K300\,\mathrm{K}. ((b)) Predict CV/NkBC_V/Nk_B and the molar CVC_V at 1000 K1000\,\mathrm{K}. ((c)) What fraction of the fully classical vibrational contribution kBk_B is realised at 300 K300\,\mathrm{K}?

Browse the problem library