# Thermodynamic Process: What Is Isobaric, Isochoric, Isothermal, Adiabatic?

## Important Formula

## What do the formula symbols mean?

## Pressure

`$$ \mathit{\Pi} $$`Unit

`$$ \mathrm{Pa} = \frac{ \mathrm{N} }{ \mathrm{m}^2 } $$`

## Volume

`$$ V $$`Unit

`$$ \mathrm{m}^3 $$`

## Temperature

`$$ T $$`Unit

`$$ \mathrm{K} $$`

## Amount of substance

`$$ n $$`Unit

`$$ \mathrm{mol} $$`

## Gas constant

`$$ R $$`Unit

`$$ \frac{\mathrm J}{\mathrm{mol} \, \mathrm{K}} $$`

*exact*value:

`$$ R ~=~ 8.314 \, 462 \, 618 \, 153 \, 24 \, \frac{\mathrm J}{\mathrm{mol} \, \mathrm{K}} $$`

Let's consider a system with an **ideal gas** in it. The state of the gas, more precisely its temperature \( T \), its pressure \( \Pi \) and its volume \(V\) are described by the ideal gas equation:

Here \(n\) is the amount of substance and indirectly describes the number of gas particles and \( R \) is the gas constant.

We refer to temperature, pressure and volume as **properties** - they describe the macroscopic state of the gas.

If we heat the gas and thus increase its temperature, we speak of a **thermodynamic process**. We could also compress the gas, thereby increasing the pressure and reducing the volume - this would also be a thermodynamic process. The thermodynamic process can be isobaric, isothermal, isochoric or adiabatic.

With an **isobaric process**, the pressure \( \Pi \) of the gas remains constant. This means that \( \Pi \), \(n\) and \(R\) are pure constants in the gas law and the volume \( V \) is proportional to the temperature \( T \). The pressure-volume diagram shows a horizontal straight line for an isobaric gas. The change in volume does not lead to a change in gas pressure.

With an **isochoric process**, the volume \( V \) of the gas remains constant. Then \(n\), \(R\) and \(V\) are constants in the gas law 1

, and the pressure \(\Pi\) is proportional to the temperature \(T\). The pressure-volume diagram shows a vertical straight line for an isochoric gas. The change in gas pressure does not lead to a change in volume.

During an **isothermal process**, the temperature \( T \) of the gas remains constant. The pressure is therefore proportional to the inverse volume: \( \Pi \sim \frac{1}{V} \). The pressure-volume diagram shows a decreasing curve for an isothermally behaving gas. Increasing the volume of the gas leads to a decrease in the gas pressure.

In the case of an **adiabatic process**, no thermal energy is transported OUT of and INTO the system. During this process, the temperature, volume and pressure of the gas can change simultaneously. The pressure-volume diagram shows a power law for an adiabatic gas. The exponent \( \gamma \) is referred to as the adiabatic exponent.