Consider a classical gas of N atoms. The Helmholtz free energy of a quantum gas made of N indistinguishable atoms, where N is a large number, is equal to F = -Nk,T|1+ In () +in 3. (2itmkpT\| h² where m is the mass of the atoms, V the volume of the container, T the temperature of the gas, kɛ is Boltzmann's constant and h is Planck's constant. Use this function to derive the equation of state for the ideal

3. The classical partition function of a gas of noninteracting indistinguishable particles is written as exp{- N! 2m Z= where N is the number of particles of mass m, r, and p, are the position and the momentum of the ith particle, B = 1/(kpT), and Tis the temperature of the gas. The volume of the gas is V. (a) Find the analytic expression of the partition function of the gas. (b) Obtain the total mean energy E of the gas from the partition function. (c) Obtain the entropy S of the gas from the partition function and the total mean energy. Lexp(-x³xdx = Va Hint:

Near the surface of a certain kind of star, approximately one hydrogen atom per 10 million is in the first excited level (n = 2). Assume that the other atoms are in the n = 1 level. Use this information to estimate the temperature there, assuming that Maxwell-Boltzmann statistics are valid.

A certain atom has a radius of 2.7 X 10-1 nm and a mass of 2.21 X 10-22 g.  What is the density of the atom? Assume that the atom is a sphere.  The volume of a sphere is given by: ?=43??3V=43πr3     where r is the radius and ?=3.14

Two stars, both of which behave like ideal blackbodies, radiate the same total energy per second. The cooler one has a surface temperature T and 4.0 times the diameter of the hotter star. What is the temperature of the hotter star in terms of T? (Just write the result)

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