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2. A gas in the cylinder An ideal gas from N indistinguishable molecules of mass m be in a cylindrical volume with base area A and height n contained on the surface of the earth (a) Within the framework of classical statistical mechanics, calculate the canonical sum of states for the system given gravity. Hints: N N! + dxx'e-ex? 4a3 ;G>0 * " 5.5 Spherical coordinates in momentum space. (b) Calculate the internal energy of the system. (c) Under what condition can the contribution of gravity be neglected? What then becomes of the internal energy? Hint: e* *1+x+ +0(x) ****0x2 (1+x)-11-x+ 0(x2) x2 1