Equation of state of an ideal gas - Isotherms of an ideal gas

Real substances show a varied and often complex behavior which is difficult to translate into a simple equation. For example, they may exist in different states or undergo phase changes; depending on the type of substance, their density varies with temperature and can increase or decrease with it.

However, for certain simplified situations it is possible to find equations of state that relate the thermodynamic variables used to describe the state of a substance. The simplest case is that of a gas.

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When a gas has low density (its molecules are very far from each other) and the interactions between its molecules are weak, we can explain its behavior using the concept of ideal gas.

An ideal gas is a theoretical model of gas whose equation of state is derived under the following hypotheses:

    • The interactions between the molecules are negligible and they only undergo elastic collisions between them.
    • The volume of the gas molecules is negligible.

The equation of state obtained by applying the above assumptions describes reasonably well the behavior of real gases for pressure and temperature conditions far from those of a change of state. That is, a pressure low enough so that the molecules are distant from each other and can therefore be considered as point particles and temperatures high enough so that the gas will not change phase to a liquid.

The equation of state of an ideal gas is given by:

where n is the number of moles and R is the ideal gas constant, whose value in SI units is:

We can graph the equation of state of an ideal gas in a PV diagram. To do so, we isolate p from the equation of state:

In this equation, we can assign different values to the temperature (in kelvin), which gives us an equation of two variables, p and V for each temperature value, for example:

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We obtain a hyperbola for each temperature value. By graphing them in a PV diagram, we get:

The curves represented are called isotherms of an ideal gas. Points on the same curve represent the states of the ideal gas (pressure and volume combinations) that are at the same temperature.

The higher the isotherm in the PV diagram, the higher its temperature.

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