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We shall be rather theoretical. It is important to be able to reduce the complexity of temperature measurement to the very simple basic idea. We will be very brief and use a kind of note-form.
Basic notion: When heat goes into a system, the entropy of the system increases.
Deductions: (i) Adiabatic changes of state do not involve heat transfer and are therefore at constant entropy. (ii) Different adiabatic lines of change are inaccessible to each other by adiabatic processes alone (the combinations of parameters of state can never be the same).
Representation: In order to get from adiabatic line (1) to adiabatic line (2), in fig. 4.5, there has to be heat transfer into the system. The increase of entropy required in order to move from (1) to (2) can be produced by any amount of thermal energy whatsoever, depending on the conditions, e.g.
Q
A
> Q
B
> Q
C
What is the connection between Q, Q, Q and the entropy increase 
S?
This is defined as: S =
( Q / T ) =
( Q / T ) =
( Q / T ),
and T is the "temperature" at which the heat transfer takes place.Measurement of T: If S is a common factor we may remove it:
( Q / T ) =
( Q / T ) =
( Q / T ), etc.
and
( ( T / T ) / T ) =
( ( Q / Q ) / Q ) etc.
This is the ideal heat engine definition of temperature.
Measurement of S: Having a measure of T we can calculate changes of entropy.
Measurements of T and S depend on our ability to realize in practice adiabatic and isothermal changes of state, and on our ability to measure quantities of energy transferred by heat. When our temperature measurements become independent of the particular properties of any substance, we are then free to use T as a means of investigating the structure and behaviour of the variety of actual systems.
The measurement of temperature: How can we describe most simply the strategy of measuring temperature? We must have at least the three following components:
(i) A definition of temperature in terms of other parameters.
(ii) Ideal systems.
(iii) Practical convenience and accuracy.
In empirical scales of temperature, the three components are fused into one. For example, on the mercury-in-glass thermometer empirical scale, temperature is defined as being directly proportional to the length of the mercury column; the behaviour of mercury is taken to be ideal (remember the elementary text book statement "mercury expands unifornily with respect to temperature"); and the criterion of accuracy is overruled by the criterion of convenience. In the International Practical Scale of temperature, the three components are kept distinct. This system of temperature measurement is still evolving because it maintains the independence of the three factors. No one type of thermometer can cover the whole range of thermal intensities. In order to use the science of thermodynamics, all the variety of practical means of temperature measurement must be brought into one consistent scheme. But this can never be made absolutely perfect.