(Answered) 1 derive strirlings approximation for n2 derive the

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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 contant 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.

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