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# Thermodynamic processes

## Thermodynamic processes overview

A thermodynamic process is the transformation of a system from an initial state to a final state. This transformation is accompanied by changes in the pressure, volume and temperature of the system.

A state is a set of values of physical quantities (e.g. volume, pressure, temperature) that describe the properties of a system.

Thermodynamic processes are represented by pressure-volume (p-V) lines/curves. They are often drawn with arrows indicating the path taken.

Several connected p-V lines/curves are often drawn on the same axes to form a cyclical process.

An example of a cyclic process: A represents an expansion at constant pressure, B represents a decrease in pressure at constant volume, C represents a compression at constant pressure, and D represents an increase in pressure at constant volume.

## Isochoric process

p-V graph showing an different thermodynamic processes (1: isothermal, 2: isochoric, 3: isobaric, 4: adiabatic).

In an isochoric process the volume is kept constant (i.e. $\Delta V=0$). This implies that the work done by the gas is zero (i.e. $W=0$).

The change in internal energy during an isochoric process is equal to the heat supplied to the system (i.e. $\Delta U=Q$).

The p-V graph of an isochoric process is a vertical line.

$p=$pressure; $Q=$heat supplied; $T=$temperature; $\Delta U=$change in internal energy; $V=$volume; $W=$work done

## Isobaric process

p-V graph showing a different thermodynamic processes (1: isothermal, 2: isochoric, 3: isobaric, 4: adiabatic).

In an isobaric process the pressure is kept constant (i.e. $\Delta p=0$). The work done by the gas is given by $p\Delta V$.

The change in internal energy during an isobaric process is given by $\Delta U=Q-p\Delta V$.

The p-V graph of an isobaric process is a horizontal line.

$p=$pressure; $Q=$heat supplied; $T=$temperature; $\Delta U=$change in internal energy; $V=$volume; $W=$work done

## Isothermal process

p-V graph showing an different thermodynamic processes (1: isothermal, 2: isochoric, 3: isobaric, 4: adiabatic).

In an isothermal process, the temperature is kept constant (i.e. $\Delta T=0$). However, there may be heat exchanged between the system and its surroundings (i.e. $Q$ is not necessarily $0$).

The p-V graph of an isothermal process is a curve. The p-V curve of an isothermal process is gentler than that of an adiabatic process.

$p=$pressure; $Q=$heat supplied; $T=$temperature; $\Delta U=$change in internal energy; $V=$volume; $W=$work done

p-V graph showing an different thermodynamic processes (1: isothermal, 2: isochoric, 3: isobaric, 4: adiabatic).

In an adiabatic process there is no transfer of heat between the system and its surroundings (i.e. $Q=0$). However, the temperature may not be constant (i.e. $\Delta T$ is not necessarily $0$).

The change in internal energy during an adiabatic process is equal to the work done on the system (i.e. $\Delta U=W$).

The p-V graph of an adiabatic process is a curve. The p-V curve of an adiabatic process is steeper than that of an isothermal process.

$p=$pressure; $Q=$heat supplied; $T=$temperature; $\Delta U=$change in internal energy; $V=$volume; $W=$work done

## Summary of thermodynamic processes

Process Characteristics
Isochoric $\Delta V=0$; $W=0$; $\Delta U=Q$
Isobaric $\Delta p=0$; $W=p\Delta V$; $\Delta U=Q-p\Delta V$
Isothermal $\Delta T=0$
Adiabatic $Q=0$; $\Delta U=W$

Thermodynamic processes are not necessarily distinct from each other.

It is possible for a thermodynamic process to be both adiabatic and isobaric ($Q=0$ and $\Delta p=0$), or adiabatic and isothermal ($Q=0$ and $\Delta T=0$).

$p=$pressure; $Q=$heat supplied; $T=$temperature; $\Delta U=$change in internal energy; $V=$volume; $W=$work done

p-V graph showing an different thermodynamic processes (1: isothermal, 2: isochoric, 3: isobaric, 4: adiabatic).