# Understanding temperature of a system of paramagnets

1. Mar 15, 2015

### hideelo

If we have some paramagnets with only two spins up or down in an external magnetic field, I understand that the entropy is maximal when the energy is 0, what I dont understand is how to think about its temperature. In some sense I know that at this preferred state the temperature is infinite, but what does that mean?

If I put a thermometer to it what will the thermometer read? I would guess (correct me if I'm wrong) nothing (or whatever its reading was before) since the paramagnet is at its preferred energy state and doesnt want to give or take any energy.

But then what does this tell me about temperature in general? In other words, what are the restrictions on the idea of "temperature is what you measure with a thermometer". More specifically, when will a thermometer NOT tell you the temperature of an object? What (if any) is the underlying similarity between all such cases where a thermometer does not tell you the temperature?

Finally, If a thermometer does not tell you the temperature in these cases, how do you empirically go and measure the temperature in these cases?

TIA

2. Mar 17, 2015

### QuasiParticle

I don't quite understand all of your questions. First of all, your system is paramagnetic material in an external field with two angular momentum states?

Entropy is maximal when all the energy states are equally occupied. The energy of the system is not zero in this case and the temperature is infinite. Infinite temperature simply means that the system will give out heat to any thermally connected system with a finite temperature. In the ground state (zero energy) entropy is zero.

A thermometer should show the temperature of the system after reaching thermal equilibrium with it (assuming the thermometer still functions at this temperature). Usually a thermometer gives incorrect readings if it hasn't reached thermal equilibrium with the measured system, or is outside its operational range.