- #1

Kashmir

- 468

- 74

"The equilibrium macrostate of a system can be completely specified by very few macroscopic parameters. For example, consider again the isolated gas of ##N## identical molecules in a box. Suppose that the volume of the box is ##V##, while the constant total energy of all the molecules is ##E##. If the gas is in equilibrium and thus known to be in its most random situation, then the molecules must be uniformly distributed throughout the volume ##V## and must, on the average, share equally the total energy ##E## available to them. A knowledge of the macroscopic parameters ##V## and ##E## is, therefore, sufficient to conclude that the average number ##\bar{n}_{s}## of molecules in any subvolume ##V_{s}## of the box is ##\bar{n}_{s}=N\left(V_{s} / V\right)##, and that the average energy ##\bar{\epsilon}## per molecule is ##\bar{\epsilon}=E / N##. If the gas were not in equilibrium, the situation would of course be much more complicated. The distribution of molecules would ordinarily be highly nonuniform and a mere knowledge of the total number ##N## of molecules in the box would thus be completely insufficient for determining the average number ##\bar{n}_{s}## of molecules in any given subvolume ##V_{s}## of the box."

The author defines equilibrium state corresponding to the "**most random situation**" .

I understand why on the average the particles are uniformly distributed throughout the volume, because the number of combinations for a uniform distribution is maximum.

But I'm having trouble understanding why using this definition of equilibrium as the most random situation how can I deduce that the average energy of a gas particle in equilibrium is ##\bar{\epsilon}=E / N##.

Where does the idea of "most random situation" enter the argument?

I'm sorry if this question is elementary. Please tell me where to go to learn if this question is too basic.

Thank you.