# Contradiction in the laws of thermodynamics?

1. Aug 27, 2011

### Maximise24

The second law of thermodynamics states that the entropy in a system, such as our universe, always increases. The third law, however, says that entropy reaches zero as a system approaches absolute zero temperature.

Our universe has been cooling off since its origin (because of its expansion), accounting for a myriad of interesting physical bodies and processes, but how is this not at odds with both thermodynamical laws? If the system that is our universe is cooling (and indeed slowly approaching absolute zero), its entropy could be said to decrease. The second law however dictates that it must increase invariably. Which is right?

2. Aug 27, 2011

### Studiot

Where did you get that?

My version says that at absolute zero the entropy of a perfect crystal is zero.

It says nothing about the approach and perfect crystals are about as common as ideal gasses or hens' teeth.

3. Aug 27, 2011

### Maximise24

I suppose my confusion comes from the seeming banality of the third law. The first two are very grand in scale and applicable to the entire universe. Why, then, does the third only say something about crystals? What's the relevance?

4. Aug 27, 2011

### atyy

5. Aug 27, 2011

### BruceW

The universe is cooling and its entropy is increasing.
But I think the reason the universe is said to be cooling is because its energy density is decreasing. (Since distant galaxies are getting further away from each other). So its not like cooling a volume of gas inside a box of fixed volume.

The forms of energy in the universe are turning from lower entropy forms into higher entropy forms. (For example, stars are burning up their fuel). So far into the future, it is possible that the structure of our current galaxy e.t.c. will no longer exist, and its contents will be strewn about in a random way. Clearly this is a higher entropy state.

6. Aug 28, 2011

### cmos

The fact/postulate that the entropy is zero at the zero of temperature is also often used, in conjunction with the Second Law, as the basis for saying that it is impossible for any system to reach 0 K. It's beyond my expertise, but I would presume that, in the theory of "infinite" expansion of the universe (note that there are other theories, e.g. the big crunch), the universe would cool to some homogeneous finite (infinitesimal?) temperature.

Furthermore, Boltzmann's equation, S=k ln W, places a strict restriction on the possible values of the entropy. Quantum mechanically, the smallest value W could have is the degeneracy of the ground state. Assuming that the universe does not have a singly-degenerate ground state, then it is impossible for the universe to ever see a zero entropy.