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The thermodynamic temperature scale comes straight from the Carnot Theorem. The Carnot Theorem states that any reversible engine working between two reservoirs has the same efficiency.

This means that ratio of the heat absorbed by the engine at the reservoir at higher temperature to the heat given by the engine at the reservoir at lower temperature is independent of the working material. Note that we have no way of measuring this temperature as yet. We know that such a quantity exists from the zeroth law of thermodynamics. We can even speak of higher and lower temperature from the direction of energy flow. However, as yet, there is no quantitative definition of the temperature. It is here that Carnot theorem is significant

We may define the thermodynamic temperature of a reservoir to be the ratio of the heat absorbed/given out by the engine at that reservoir to the heat absorbed/given out by the engine at a reference reservoir which we say is at unit temperature.

It may be shown that the thermodynamic temperature scale coincides with the ideal gas temperature scale.

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