Suppose I have a box containing particles and be left alone, with a total amount of energy, E. Hence, at equilibrium, these particles will obey the Maxwell-Boltzmann distribution. The entropy of the system is,(adsbygoogle = window.adsbygoogle || []).push({});

[tex]S=NkT lnV[/tex]

where T is the temperature of the system. V = volume of box.

Suppose now, I divide this box equally into two, hence, now, each new box's volume is V/2, and the number of particles in each box is just N/2. But the temperature of these two new systems will stay the same, since they were in equilibrium initially.

Now, the new entropy of both systems would be:

[tex] S_{new}=\frac{N}{2}kTln V/2 + \frac{N}{2}kTln V/2 [/tex]

[tex] S_{new} = NkT ln V - NkTln 2 [/tex]

But, [tex]S_{new} < S[/tex]

Where did I go wrong?

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# Box containing particles and be left alone

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