# A-level Chemistry/AQA/Module 5/Thermodynamics/Temperature and the Zeroth Law

## Temperature and Thermal EquilibriumEdit

Seems appropriate start talking about thermodynamics defining the concept of Temperature, however we should first note some intuitive notions from everyday life.

First of all, humans have awareness of temperature; we can sense cold and hot things, and we historically set a numerical value to that sensation (we'll see later how).

Then, we have to look at how evolve temperature. Let say that we have two litres of water separated and at different temperatures, say ${\displaystyle T_{1}}$ and ${\displaystyle T_{2}}$. When we mix them, together they will get to a new temperature, ${\displaystyle T_{3}}$, such that ${\displaystyle T_{1}. So, we can say that the evolution of temperature have a direction towards equality. Note that although is not always this way, we are saying that a whole body have a temperature, so the two litres together are a perfect mix between the two litres separated.

We don't need to mix bodies to have equality of temperatures; experience tell us that bodies touching each other tend to equalize. So, we can say that two bodies are at the same temperatures when they don't change temperature if touching each other. It may seem obvious, but it's worth to put it that way. We are talking here of Thermal Equilibrium.

## Zeroth Law of ThermodynamicsEdit

As a direct consequence of the definition of thermal equality, is that temperature measure is transitive; so, if we have three bodies, A,B and C, such that

${\displaystyle T(A)=T(B)}$

and

${\displaystyle T(B)=T(C)}$

then

${\displaystyle T(A)=T(C)}$.

This is known as Zeroth Law of Thermodynamics.

## The ThermometerEdit

We should say that this property allow us to build a thermometer, if we are able to translate temperature to a repeatable numeric value. In the above example (two litres of water evolving to a new temperature), we used the same quantity of water. The temperature scale is based in taking the final temperature as

${\displaystyle T_{3}={\frac {T_{1}+T_{2}}{2}}}$

for different masses of water we would have the weighted average

${\displaystyle T_{3}={\frac {m_{1}T_{1}+m_{2}T_{2}}{m_{1}+m_{2}}}}$

By changing the masses of water of known temperatures ${\displaystyle T_{1},T_{2}}$ we could achieve by this mechanism every temperature between them and calibrate another (more comfortable) device that translates temperature to a repeatable numeric value. The most common device of this kind is the mercury thermometer, which is practically a bulb connected to a thin tube (a capilar). It was seen that the space that the mercury occupies in the tube increases with temperature lineally, so

${\displaystyle l-l_{0}=l_{0}\alpha (T-T_{0})\,}$

where ${\displaystyle l}$ is the occupied space, and ${\displaystyle l_{0}}$ is the space occupied at a reference temperature ${\displaystyle T_{0}}$; ${\displaystyle \alpha }$ is a constant (the linear thermal expansion coefficient). Celsius chose the temperatures ${\displaystyle T_{1},T_{2}}$ as the temperatures of solidification and condensation of water, setting them as ${\displaystyle 0}$ and ${\displaystyle 100}$ and took the measure of a degree as a division of this range by 100. Fahrenheit instead, used the temperature of freezing brine as the ${\displaystyle 0}$ of the scale and the human temperature as 96 (the water solidification was set to 32°F). Later this scale was modified to have the condensation of water exactly 180°F above the solidification.

Note that to build a temperature scale, one used a thermal stable mixture, a mixture that maintain constant temperature for a while. This is easily achieved using a compound which is changing state, like melting ice: the water is at the temperature of the ice, because they are at thermal equilibrium; the water then tend to get hotter (to reach equilibrium with air), and also the ice is in this process; when the ice melts, it turns into more water, that stabilizes the equilibrium with the existing water. Additionally, it was seen that there's an anomaly at change of states: thermal equilibrium between water and ice, for example, can be reached above (liquid) or beneath (solid) the solidification temperature, but also at the very solidification temperature, having as the final product a mixture between liquid and solid, or just liquid or just solid. This phenomenon is known as latent heat, and will be described further.

We have not given yet a definition of temperature. That's another story.