Discuss the below:
1 Derive Strirling's approximation for N!.
2 Derive the Gaussian approximation of the binomial distribution.
3 Derive expressions for the mean and standard deviation for the binomial distribution.
4 Compute the pressure of an ideal Bose gas at absolute zero.
5 Compute the entropy of an ideal gas using the micro-canonical ensemble.
6 Compute the internal energy of N harmonic oscillators as a function of temperature using the micro-canonical ensemble.
7 Compute the susceptibility of a spin 1/2 particle .
8 Compute the entropy of a harmonic oscillator.
9 Compute the energy fluctuations of a system at constant temperature.
10 Compute the internal energy of a diatomic molecule.
11 Estimate the maximum possible height of trees.
12 Compute the temperature of the relic neutrino background of the universe.