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Thermodynamic Temperature Scales

This tie-fighter diagram shows a heat engine operating between a hot thermal reservoir at TH and a cold thermal reservoir at TC. The heat engine absorbs heat QH from the hot reservoir, rejects heat QC to the cold reservoir and produces work, W.

What if we know the temperature of one thermal
reservoir and we measure QH, QC, and W from
our reversible HE experimentally?
Then, we could calculate η and, if we knew how η depended on TC and TH, we could determine the temperature of the other reservoir !
This would allow us to construct a temperature scale that does not depend on the working fluid or the properties of any substance. This type of temperature scale is called a Thermodynamic Temperature Scale.
The objective of this lesson is to determine the functional dependence of η on TC and TH and to use it to develop a Thermodynamic Temperature Scale and to explore how such a scale is related to other temperature scales.

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Lesson 6F: page 2 of 16

Whoa ! What do Carnot Cycles have to do with something as fundamental as an absolute temperature scale, such as the Kelvin scale ?
Think about the Carnot HE shown here.
Let’s say we know TH and we want to determine TC.
It isn’t difficult to measure QH, QC and W, but what do we do with them ?
Well, we can calculate the efficiency of the Carnot HE, right ?
Then, IF we knew the equation h = a function of TH and TC, we would have one equation in one unknown and we could solve for the unknown value of TC.
So, if we arbitrarily make up a value for TH, we can use our Carnot Cycle to construct a NEW temperature scale that does NOT depend on the properties of ANY substance !
This type of temperature scale is called a Thermodynamic Temperature Scale.
So, all we need to do is determine the function that relates h to TH and TC and we can crank out as many thermodynamic temperature scales as we like.
Let’s get on it.

Thermodynamic Temperature Scales

Ch 6, Lesson F, Page 2 - Thermodynamic Temperature Scales