A little excercise

In problem T06.2, we calculated the work differential for an ideal gas in a power-potential trap.
1. How can we use the result to obtain DW for an ideal gas in a 3D container? What is the interpretation of the parameter "a" in that case.
2. What do we get for DW for d=3 and n --> infinity? And how is this result related to the expected form DW = N k_B T dV/V ?
Try to answer these questions before Friday at noon. Post your solutions. You will get extra points for correct solutions.

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Work for an ideal gas in a 3D container (corrected)

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Using the differential al work calculated on exercise 6.2: 1. How can we use the result to obtain DW for an ideal gas in a 3D container? What is the interpretation of the parameter "a" in that case. Solution.  The differential of work calculated on exercise 6.2 is Here, d represents the dimension of the box. So The parameter a is the lenght, according to equation (67). Because we are working on  3 dimensions, a³=V . This might come from the definition of entropy*.      2. What do we get for DW for d=3 and n --> infinity? And how is this result related to the expected form DW = N k_B T dV/V?    Solution.  On the last expression we get DW for three dimensional case. Now, applying the limit on infinity, we expect that the differential of work would become on well potential one. So,   
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homework T06.3, a) and b)

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