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

Important Formula

Formula: Ideal Gas Law

$$\mathit{\Pi} \, V ~=~ n \, R \, T$$ $$\mathit{\Pi} ~=~ \frac{n \, R \, T}{V}$$ $$V ~=~ \frac{n \, R \, T}{\mathit{\Pi}}$$ $$T ~=~ \frac{V \, \mathit{\Pi}}{n \, R}$$ $$n ~=~ \frac{V \, \mathit{\Pi}}{R \, T}$$ $$R ~=~ \frac{V \, \mathit{\Pi}}{ n \, T }$$

Rearrange formula

What do the formula symbols mean?

Pressure

$$ \mathit{\Pi} $$ Unit $$ \mathrm{Pa} = \frac{ \mathrm{N} }{ \mathrm{m}^2 } $$

This pressure is present in a confined system containing an ideal gas. According to the ideal gas law, the pressure increases when the temperature $T$ of the gas increases or the volume $V$ in which the gas is confined decreases.

Volume

$$ V $$ Unit $$ \mathrm{m}^3 $$

The volume of a closed system containing an ideal gas.

Temperature

$$ T $$ Unit $$ \mathrm{K} $$

It is the absolute temperature (in Kelvin) of the gas in a closed system.

Amount of substance

$$ n $$ Unit $$ \mathrm{mol} $$

The amount of substance indirectly indicates the number of gas particles. It is related to the particle number $N$ by the Avogardo constant $N_{\text A}$: $ n = \frac{N}{N_{\text A}} $.

Gas constant

$$ R $$ Unit $$ \frac{\mathrm J}{\mathrm{mol} \, \mathrm{K}} $$

Molar gas constant (also called universal gas constant) is a physical constant from thermodynamics and has the following 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:

$$ \begin{align} \mathit{\Pi} \, V ~=~ n \, R \, T \end{align} $$

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.

Isobaric, Isochoric, Isothermal and Adiabatic Process on the p-V Diagram

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.

Isobaric, Isochoric, Isothermal and Adiabatic Process on the p-V Diagram

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.

Isobaric, Isochoric, Isothermal and Adiabatic Process on the p-V Diagram

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.

Isobaric, Isochoric, Isothermal and Adiabatic Process on the p-V Diagram

Adiabatic Process in a Pressure-Volume Graph