Zeroeth Law of Thermodynamics

Let's just state the zeroeth Law of Thermodynamics

If bodies $A$ and $B$ are in thermal but not mechanical contact and heat flows from $A$ to $B$ and if $B$ is in thermal contact with $C$ and heat flows from $B$ to $C$ then

Heat will flow from $A$ to $C$ if they are in thermal contact. In other words,

$$\input{equations/zero-law-1}$$ (03-3)

$$\input{equations/zero-law-2}$$ (03-4)

We can call the body $B$ a thermometer and use the zeroeth law.³

The temperature can be related to $\Theta$, we can just call $T=\Theta$. This can be done rigorously and it defines an absolute zero ( $T=0$) but let's not do this and move on.

Later we may use the entropy, $S$ and internal energy, $U$, of a body to define the temperature.⁴

$$\input{equations/Tdef}$$ (03-5)

For a body that does no work, or has no work performed on it, the temperature is the rate at which internal energy changes with entropy.

$$\input{equations/Tdef-alt}$$ (03-6)

$U$ tends to increase with $S$.

In this lecture, we have discussed state variable that gives us information about a body, an efficient way.

All of these quantities rely on measurement but are assumed to be independent of the type of measurement.