A major step in the development of our understanding of thermodynamics was the overturning of the phlogiston theory that assumed that "heat" was a fluid that was conserved and could be moved from one object to another. The subtler idea that heat was the realization of energy in a particular form and could therefore be created by translation from other forms of energy, say by friction, conquered the phlogiston idea in part because of Count Rumford's experiments. In one series of experiments he showed that motion could be converted to heat through friction (not that friction just extracted heat that already existed in the objects) and that heat did not have a measurable weight.
But today we know that not only is "heat" (the thing measured by a thermometer) a form of energy, so is mass, and therefore, by extension, "heat" must have weight. Einstein's famous equation, E = mc2, gives the connection. Therefore, we can ask the question: "How much does one degree of temperature weigh?" We know from our study of kinetic theory that
3/2 kBT = average KE of 1 molecule.
You might also have seen the useful mnemonic (if not, here's a great place to learn it) that
at STP (T ~ 300K), kBT = 1/40 eV.
From this, we ought to be able to infer the "weight" of 1 degree of temperature.
This isn't really quite legit. Temperature represents a density of energy -- an amount per molecule. What we should really therefore be calculating is the amount of energy a temperature change corresponds to in some amount of some material. Rumford tried to measure the change in the weight of water due to the loss of "heat" as it cooled from 61oF to 34oF. What is the weight of the thermal energy lost by 1 kg of water in Rumford's cooling, according to Einstein?
Joe Redish
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