1.

Find the mathematical and the thermodynamical probabilities of the five possible distributions of four balls in two halves of a vessel (Fig.), assuming them to be distinguishable.

Answer»


Solution :Imagine the balls to be designated by the letters a, b, c, d. Write out all the possible distributions of the balls in both HALVES of the vessel (Table ). We see that there are altogether `2^4 = 16 `distributions, the first and the fifth of which may be realized in one way, the second and the fourth in four WAYS, the third in six ways. These DIRECTLY give us the thermodynamic probabilities.
To obtain the mathematical probabilities, divide the values obtainted by the total NUMBER of cases.
Use the data OBTAINED to compile Table 18.4b, which shows the thermodynamic and mathematical probabilities of interest to us.


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