- #1
touqra
- 284
- 0
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,
S=NkT lnV
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:
S_{new}=\frac{N}{2}kTln V/2 + \frac{N}{2}kTln V/2
S_{new} = NkT ln V - NkTln 2
But, S_{new} < S
Where did I go wrong?
S=NkT lnV
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:
S_{new}=\frac{N}{2}kTln V/2 + \frac{N}{2}kTln V/2
S_{new} = NkT ln V - NkTln 2
But, S_{new} < S
Where did I go wrong?
Last edited:
