Skip to main content
Library homepage
 

Text Color

Text Size

 

Margin Size

 

Font Type

Enable Dyslexic Font
Engineering LibreTexts

25.2: Thermodynamics

( \newcommand{\kernel}{\mathrm{null}\,}\)

Here we shall go through the basic thermodynamics that lies behind use of the Ellingham diagram. First, we will establish the link between the thermodynamics of a reaction and its chemistry.

The Gibbs free energy, G, of a system can be described as the energy in the system available to do work. It is one of the most useful state functions in thermodynamics as it considers only variables contained within the system, at constant temperature and pressure.

It is defined as:

G=HTS

Here, T is the temperature of the system and S is the entropy, or disorder, of the system. H is the enthalpy of the system, defined as;

H=U+pv

Where U is the internal energy, p is the pressure and v is the volume.

To see how the free energy changes when the system is changed by a small amount, we can differentiate the above functions:

dG=dHTdSSdT

and;

dH=dU+pdv+vdp

From the first law,

dU=dqdw

and from the second law

dS=dqT

we see that,

dG=dqdw+pdv+vdpTdS+SdT

=dw+pdv+vdpSdT

=vdpSdT

Since work, dw = pdv

The above equation shows that if the temperature and pressure are kept constant, we see that the free energy does not change. This means that the Gibbs free energy of a system is unique at each temperature and pressure.

At a constant temperature dT = 0 and so

dG=vdp

We can find G for the system by integration. To do this we need the system’s equation of state, to give a relationship between v and p.

We will consider an ideal gas. For one mole of an ideal gas the equation of state is;

v=RTp

so

dG=RTdpp

Integrating:

GRTln(p)+const.

This we can express as

G=Go+RTln(ppo)


This page titled 25.2: Thermodynamics is shared under a CC BY-NC-SA 2.0 license and was authored, remixed, and/or curated by Dissemination of IT for the Promotion of Materials Science (DoITPoMS) via source content that was edited to the style and standards of the LibreTexts platform.

Support Center

How can we help?