# State Variables

A thermodynamic system has to be macroscopic (having a sufficient larger size); this eases measurement of its properties such as;

Pressure

Volume

Temperature

Composition

Density

Such properties are consequently called macroscopic or bulks. These properties are also called state or thermodynamic variables. They do not rest on the past history of the system. A state variable which rest on other variables is called a dependent variable; while, that, which did not on dependent on other variable, are called independent variables. Using ideal gas equation for example.

The ideal gas equation is written as;

This equation tell us that V only change when the is change in the T, n and P, as such V is refer to be a dependent variable, whereas n, T and p are called independent variables because V depend on them.

A typical example is child and their parent, a child depend on his parent to survive, where parent have to struggle to take care of the child, as such,

The child is called dependent, while the parent which the child depend on is called independent

We know that R is the gas constant. On the other hand, if you write this equation as,

Therefore p become the dependent variable, while n, T arid V are independent variables. The decision of dependent and independent variables is a matter of suitability.

## State of a System

System state is defined when the state variables have fixed values. It is compulsory to identify all the state variables since these are interdependent. For exam if the system is an ideal gas, then its pressure, volume, temperature, and the amount of the gas (number of moles) are correlated by the gas equation. Thus, if we identify three of these; the fourth variable is automatically become fixed. Likewise many of its other properties like density, heat capacity etc. is also fixed although via a more complex relations.

Self-Assessment Exercise

Identify the type of system in each of the following cases:

1) A beaker covered with a lid?

2) A beaker without lid?

1. Close system
2. Isolated system
3. Open system