4. Equation of state

After we have learned what temperature is and how it can be measured, let's look at heat phenomena in more detail. Many phenomena can be discovered without any physical devices. An ordinary rubber ball, if you take seriously the observation of the air dynamics inside it, will allow you to come to important conclusions.

The ball, and therefore the air inside it, has a certain volume \( V \). This volume characterizes the condition of the air in the ball. Volume is one of the values that characterize the state of any macroscopic body.

The ball, like any other body, can be located in different external conditions. If you lift it up on a high mountain, the ambient air pressure on the ball-walls will decrease. After all, the atmospheric pressure decreases with height. This will cause the ball to inflate. The air pressure \(p\) inside it will become less as the volume increases. Conversely, if you squeeze the ball with your hands (carefully so that it does not explode), its volume decreases and the pressure inside increases.

The connection between the volume of air inside the ball and its pressure is, of course, obvious and understandable to everyone. All we have to do is try to notice the general pattern here.

The two values that characterize the condition of the air in the ball (volume and pressure) depend on each other. Pressure is another value (along with volume) that characterizes the state of the body.

Let's not forget the temperature. If you put an ice cube inside the ball and then inflate it, the following happens. The ice cube will melt and the ball will start to "lose weight". The air pressure in it and the volume will begin to decrease. It is clear it happens by changing the temperature in the ball.

From these simple observations, it can be concluded that there is a connection between the volume, pressure and temperature of the air in the ball. And this is true not only for the air in the ball, but also for any gaseous, liquid and solid body.

The equation that defines the relationship between temperature, volume and pressure of bodies is called the equation of state.

Each system - gas, liquid or solid - is characterized by its own equation of state. In some cases ( for instance, sparse gas) the equation of state is simple, in others (for instance, water) it is very complicated.

The knowledge of the equation of state is very important in the research of heat processes. It allows you to answer three groups of different questions in full or in part.

The equation of state makes it possible to determine one of the state values, for example temperature, if two other values are known. This is what is used in thermometers.

Knowing the equation of state, we can say how different processes will run under certain external conditions. For example, how would the gas pressure change during heating if its volume remains constant? What would happen to the gas pressure if its volume were to be increased with the same temperature, and etc.

Finally, knowing the equation of state, it is possible to determine how the state of the system changes if it performs work or receives heat from surrounding bodies.

All of this will be discussed later. First, let's see how we can experimentally identify the equation of state for gas.