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Skip to 0 minutes and 3 seconds Euclid was a philosopher and mathematician who lived more than 2000 years ago. He developed ten axioms in his book Elements. An axiom is a statement which is so evident that it can be accepted as a truth without controversy. Euclid’s first axiom was that things that are equal to the same things are equal to each other. If you express this in terms of thermal equilibrium, then it’s the zeroth law of thermodynamics. But this wasn’t recognised until about 1850, probably by William Rankin, a Scottish civil engineer. Euclid’s version was things that are equal to the same things are equal to each other.

Skip to 0 minutes and 42 seconds In thermodynamics, we restrict this to two systems in thermal equilibrium with a third must also be in thermal equilibrium with each other. Thermal equilibrium means that there are no differences, or no unbalanced potentials. So if we look at my coffee here, this is quite hot. And if I pour my coffee into a pair of cups, then if we ignore any heat losses that have occurred whilst I’ve been pouring the coffee, we can say that the coffee in this cup is in thermal equilibrium with the coffee left in the pot, and the coffee in this cup is in thermal equilibrium with the coffee left in the pot.

Skip to 1 minute and 27 seconds And so we can also deduce that the coffee in the two cups must be in thermal equilibrium with each other. And that’s the zeroth law of thermodynamics. The zeroth law is important in thermodynamics because it implies that there’s a property that measures or indicates thermal equilibrium. We call it temperature. We use temperature to define heat transfer. Heat transfer is the exchange of thermal energy, which occurs between two systems that are not in thermal equilibrium. The energy flows from hot to cold, so my coffee is moving towards thermal equilibrium with the surroundings.

Skip to 2 minutes and 8 seconds The zeroth law leads to the definition of temperature and heat transfer. The understanding of heat transfer as a thermal energy exchange is needed to establish the equivalence of work and heat that underpins the first law of thermodynamics.

# The Zeroth Law and Thermal Equilibrium

From Euclid’s first axiom, via hot coffee, to the Zeroth Law of Thermodynamics which leads to the concepts of heat and temperature.