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**Unformatted text preview: **3. (25 points) Calculate the entropy of an ideal gas of N particles each of mass m at temperature T confined to a one dimensional line of length L. [Stirlings formula: ln N! ~ N ln N N when N is very large] 4. Calculate the efficiency of a heat engine made of an ideal monatomic gas running on a complete cycle made of two isothermal paths one at T h (1 2) and the other at T c (3 4) and two equal volume paths at V 2 (2 3) and V 1 (4 1) as shown in the diagram. Compare this with the efficiency of a Carnot engine operating at these two temperatures. [You may wish to give your answer in inverse efficiency which is simpler.] (30 points) Note : You need to explain every step in your derivations. You won't get any credit if you just copy the results from your formula sheet. The following information may be useful: Avagadro's number N A = 6.022 x 10 23 per mole Boltzmann constant k B = 1.38 x 10-23 J/K Planck's constants h= 6.63 x 10-34 Joules- sec...

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