State Variables

We are all familiar with the concept of temperature. The Zeroth Law of Thermodynamics formalizes our intuition and experience as follows:
“If a system A is in equilibrium with system B (that is, has no exchange of heat with it), and if system B is in equilibrium with system C, then A is in equilibrium with C”.
This law allows us to associate a quantity called temperature to each system in thermal equilibrium, so that two systems in equilibrium have the same temperature. The thermometer is a device that uses the Zeroth Law in a quantitative and practical way. Note: We will use the absolute temperature scale where units are measured in Kelvins. The conversion from Celsius, $t$ to Kelvin $T$ is : $T = t + 273.15$. In addition to the temperature, one may need more thermodynamic parameters, called state variables, to completely characterize the state of the system. For example, for a gas these are the pressure $P$ and volume $V$. Variables such as temperature and pressure that are independent of the size of the system are called intensive, while those such as the volume are called extensive. The parameters that can be used to describe a system are not all independent but related by an equation of state. For an ideal gas one has the equation

$$PV=NkT$$ (4.1)

where $k=1.38 \times 10^{-23}$ Joules/K is called Boltzmann’s constant, and $N$ is the number of molecules. As you must have learnt in school, an ideal gas is the universal limiting description of real gases when their density is very low and the temperature high. In general, the equation of state of a real substance is more complicated. It is usual to plot the equation of state as a function of its parameters. One useful curve follows by keeping $V$ constant and representing the equation of state on a $P-T$ plot as shown in the figure for a generic substance. The lines mark boundaries between the different phases of the substance, where changes occur in the physical properties of the substance.