A physics professor from the Universidad de Sevilla (University of Seville) has tackled a problem in thermodynamics that has been around for more than a century, offering a new proof that also challenges an idea once put forward by Albert Einstein.
José María Martín Olalla’s study, published in The European Physical Journal Plus, focuses on the Nernst heat theorem. This theorem, first stated in 1905, says that as temperature gets closer to absolute zero, the exchange of entropy (a measure of disorder) also gets closer to zero. In his paper, Martín Olalla shows that the theorem can be proven using only the second law of thermodynamics, which says that the entropy of the universe always increases.
The proof defines the condition T=0 using something called a Carnot thermometer. This way of defining absolute zero does not depend on whether specific heats vanish or whether absolute zero can be reached in practice. According to the study, this approach broadens the reach of the second law and narrows the third postulate of thermodynamics to one statement: the entropy of a finite-density, chemically homogeneous body must not be negative.
The debate over the Nernst theorem began in the early 1900s, when scientists studied how matter behaves near absolute zero (–273°C). Walther Nernst, who won the 1920 Nobel Prize in Chemistry, argued in 1912 that absolute zero could never be reached. He said that if it could, someone could build a machine that used absolute zero as a coolant to turn all heat into work, which would break the rule of increasing entropy.
Einstein disagreed, saying such a machine could never be built in reality, so it posed no threat to the second law. He separated the Nernst theorem from the second law and linked it to a third, independent principle.
Martín Olalla’s proof brings the hypothetical machine back into the discussion but with a twist. He says the second law requires the machine to exist in a “virtual” form, meaning it would not consume heat, produce work, or break any thermodynamic rules. Combining this with the Carnot thermometer definition leads to the conclusion that entropy exchanges approach zero as temperature approaches absolute zero, and that absolute zero cannot be reached.
“A fundamental problem in thermodynamics is distinguishing the sensation of temperature, the sensations of hot and cold, from the abstract concept of temperature as a physical quantity,” Martín Olalla said. “Formally, the second law of thermodynamics provides a more concrete idea of what the natural zero of temperature is. The idea is not related to any sensation, but to that machine imagined by Nernst but which has to be virtual. This radically changes the approach to proving the theorem.”
The study also points out that the only general property of matter near absolute zero not tied to the second law is the vanishing of heat capacities, noted by Nernst in 1912. Martín Olalla calls this “more like an important addendum than a new principle.”
He said his thermodynamics students were the first to see the proof. “I hope that with this publication the proof will become better known, but I know that the academic world has great inertia,” he said.
Source: Universidad de Sevilla, Springer Nature
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