pranav_bhrdwj said:
Also I'm curious to understand your way of falsifying the third law. I would be grateful if you explain it to me in a bit more simpler terms (I'm yet to complete my bachelors in physics) !
Thanks !
First, understand that I was speculating. To understand what I was saying, let's reduce that Third Law of Thermodynamics to differential equations and inequalities. Instead of mucking around with visualization, let us try to express the Third Law mathematically. Once we have a mathematically formal way to express the Third Law, then we can think about experimental ways to falsify or validate it.
I don't have any references that precisely express the Laws of Thermodynamics the way I showed you. However, there are plenty of textbook examples which use equations like them.
One way to express the Third Law is by stating that the entropy of a closed system is at a minimum at zero absolute temperature. Let us write some differential equations equivalent to that.
The entropy of a closed system near equilibrium is a function of state variables including absolute temperature. That is,
1) S=S(T,P,V,{u_i})
where for the closed system T is absolute temperature, P is pressure, V is volume, u_i is the i'th state variable and {u_i} is a complete set of such state variables. The entropy S is a continuous function of T. Basically, equation 1 is equivalent to saying entropy is a perfect differential in terms of reversible processes. However, I promised not to go deeply into visualizations.
The second law states that the total entropy of a system must never decrease, and that the entropy can never spontaneously flow from a high temperature system to a low temperature system. The second law is basically equivalent to the statement that if,
2) T>0,
then,
3) ∂S(T,P,V,{u_i})/∂T>0.
Equations 2 and 3 are mathematically formal expressions for the second law. The more visual expressions for the third law can be derived from equations 2 and 3, provided we carefully define what a system variable is. However, I think you can roughly see how 2 and 3 is approximately equivalent to the other expressions of the second law.
From introductory calculus, one knows how to find the minimum of a function. If S is at a relative minimum at T=0, then,
4) ∂S(T,P,V,{u_i})/∂T=0,
and,
5)∂^2 S(T,P,V,{u_i})/∂T^2 > 0.
The last two equations are mathematical expressions for the third law. One can see that finding absolute zero is basically the same as finding the minimum of the function, S. Because of the second law (equation 3), one can see that there is only one relative minimum in S. There is only one zero absolute temperature.
If you look at number 4, you see that one needs an infinitely large
change in entropy to produce a finite change in temperature at T=0. This is basically the third law.
Of course, these mathematical equations have several physical hypotheses hidden in them. I haven't told you how to measure S, for instance. However, I hope that you get my point. The Four Laws of Thermodynamics (0, 1,2, 3, 4) are quantitative theories. They are used to define differential equations with quantitative solutions.
To falsify the Third Law, you have to show that in the limit of T=0,
6) ∂S(T,P,V,{u_i})/∂T≠0.
Experimentally, one would determine S as a function of T for any fixed set of state variables. If one can determine that at T=0, equation 6 is probably true, then one has proven that the Third Law is probably false.
I can rewrite these equations several says. However, proving the Third Law of Thermodynamics is true is basically proving that equations 4 and 5 are true. Experimentalists have to deal with uncertainties and tolerances, which is why I tried to explain the procedure in the way I did. A good experimenter never absolutely proves something, he proves something to within a certain tolerance. But without going through grungy statistical details, the experimenter would try to prove equations 4 and 5 as T approaches 0. One is measuring the slope of the S versus T curve. One extrapolates to T=0.
