PPT Slide
1. Problem nr. 1 (Free energy of a two state system) on page 81
2. Problem nr. 2 (Magnetic susceptibility) on page 81
3. Problem nr. 3 (Free energy of a harmonic oscillator) on page 82
4. Problem nr. 4 (Energy fluctuations) on page 83
Consider a closed thermodynamic system (N constant) with fixed temperature (T) and volume (V). By using the Renyi entropy formula, the expression for the probability of one state, and the fact that F=U-TS, prove, that F=-kBTln(Z)
Equipartition of energy for ideal gases
- in an ideal gas for all possible degrees of freedom the average thermal energy is: ?/2 (kT/2)
- generalization: whenever the hamiltonian of the system is homogeneous of degree 2 in a canonical momentum component, the classical limit of the thermal average kinetic energy associated with that momentum will be ?/2
degrees of freedom for one molecule:
- molecules composed by one atom: 3 --> motion in the three direction of the space
- molecules composed by two atom: 7 --> motion of the molecule in the three directions of space + rotations around the two axis perpendicular to the line connecting the two atoms + vibrations (kinetic and potential energy for this)
degrees of freedom for the system: N x degrees of freedom for one molecule
Heat capacity at constant volume of one molecule of H2 in the gas phase