Question

a.) What does a partition function represent in statistical thermodynamics? A. The number of rotational symmetry elements of a molecule with more than 2 atoms. B. The number of thermally accessible energy levels at a given temperature. C. The number of molecules that partition themselves between the liquid and the gas phase of a substance b.) The constant volume heat capacity for a monoatomic gas is equal to: A. RT B. R C. 32 RT D. 3/2 R c.) The residual entropy for a molecule that can assume 6 possible orientations of equal energy in its crystal lattice is equal to A. k In (6) B. k In (NoN) C. k In (N6) D. Zero d.) To find a compact expression for the translational contribution to the molecular partition function the sum over all energy levels was replaced with an integral. This approach is justified, because A. Energy spacings are very small compared to kT B. There is no quantum model for translational motion. C. The energy levels are all non-degenerate. D. The term exp(-& B) approaches zero for all energy levels above the ground state.

Answer 1

A energy spacing's are very small compared to KT transitional partition function is given by q = sigma_nx sigma_ny sigma_nz exp[-h^2/8 m k T(n_x^2/a^2 + n_y^2/b^2 + n_z^2/c) The spacing between the energy levels of a particles in a three dimensional box is very small compared with thermal energy kT This equation is given by neglecting degeneracy hence summation is replaced by integration