As far as I can tell, the concept of entropy is a purely statistical one. In my engineering thermodynamics course we were told that the second law of Thermodynamics states that "the entropy of an isolated system never decreases". However, this doesn't make much sense to me.
By counter-example: Consider a gas-filled isolated system where the gas has maximum entropy (it is at equilibrium). Since the molecular motion is considered to be random, at some point in the future there will be a pressure gradient formed by pure chance. At this point in time, entropy has decreased.
According to Wikipedia, the second law purely states that systems tend toward thermodynamic equilibrium which makes sense. I then ask a) is the second law as we were taught it wrong (in general), and b) what is the use of entropy (as a mathematical value) if it's effectively an arbitrary definition (i.e. what implications can we draw from knowing the change in entropy of a system)?
Thanks in advance for your help.
Best Answer
Violations of the second law are possible. The law is probabilistic, not absolute or fundamental. In your example, small pressure differences $\Delta p$ will always exist. These will fluctuate randomly about a mean of zero. Because the number of particles is something like Avogadro's number, the probability is extremely high that $\Delta p/p$ will be extremely small -- much too small to be measured with a macroscopic device such as a pressure gauge.
It's right in the sense that you could spend the rest of your life watching for a detectable $\Delta p/p$, and the rest of the human race could also devote their own lives to similar observations, and there would be no meaningful probability that any of you would ever see what you were looking for.
What do you mean by arbitrary? It doesn't seem arbitrary to me at all.
Historically, the entropy concept was invented precisely because it was useful. It was useful for understanding limits on the efficiency of steam engines.