Tarea T05
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Work for an ideal gas in a 3D container (corrected)
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,
Profesor, no entiendo que es lo que tenemos que hacer, ya que en el microcanonico usamos la energía y en el macrocanonico usamos la temperatura, cómo lo comparamos?
ResponderBorrarEn ambos casos obtienes una relación entre energía y temperatura. Esta relación debe ser la misma
ResponderBorrarGood afternoon Dr.Gorin
ResponderBorrarI have a question, in the T05.3 a)
Do you want us to calculate the probability for an especific spin chain, or to calculate the probability for one single spin to be one?
In the second case we can consider as conditional probability?
In (a) you should calculate the probability for one single spin.
BorrarIn (b) you should realize that the spin states are statistically independent among each others. So one can generate a random configuration of N spins choosing each spin state at random independent of all others. The idea is, generate a large sample of random configurations and calculate the required quantities for that sample.
Thanks for the answer, but I think I didn't understand it well.
BorrarIn (a) we have to calculate the probability for a single spin chain? or, we have to calculate the probability for a spin in a N-spin chain?
For a single spin in the chain!
BorrarGood morning. Excuse me, should we send the homework by e-mail?
ResponderBorrarJosé Luis has sent you a link to upload your homework. Here, it is again:
Borrarhttps://drive.google.com/drive/folders/1zyNpoTXpVp8I2hqmw3wEd9SbnSkJmXX-?usp=sharing