1.14.16: Energy and First Law of Thermodynamics
A central axiom of chemical thermodynamics is that a given system has a property called energy. In fact the First Law of Thermodynamics centres on the concept of energy. In its broadest terms, the law requires that the energy of the universe is constant [1]. This is a rather overwhelming statement. A more attractive statement is that the thermodynamic energy \(\mathrm{U}\) of a typical chemistry laboratory is constant.
\[\mathrm{U} = \text{ constant} \label{a} \]
The latter is the principle of conservation of energy; energy can be neither created nor destroyed. A chemist ‘watches’ energy “move” between system and surroundings. As a consequence of Equation \ref{a} we state that,
\[\Delta \mathrm{U}(\text { system })=-\Delta \mathrm{U}(\text { surroundings }) \label{b} \]
We cannot know the actual energy \(\mathrm{U}\) of a closed system although we agree that it is an extensive property of a system. In describing the energy changes we need a convention. We use the acquisitive convention, describing all changes in terms of how the system is affected. Thus \(\Delta \mathrm{U} < 0\), means that the energy of the system falls whereas \(\Delta \mathrm{U} > 0\) means that the energy increases [2]. In the context of chemistry, chemists agree that the energy of a given closed system can be increased in two ways:
- heat \(\mathrm{q}\) passing from the surroundings into the system, and
- work \(\mathrm{w}\) done by the surroundings on the system. In a wider context the concept of energy is linked with the First Law of Thermodynamics which is based on the following axiom.
\[\Delta \mathrm{U}=\mathrm{q}+\mathrm{w} \label{c} \]
As it stands the symbols \(\mathrm{U}\), \(\mathrm{q}\) and \(\mathrm{w}\) seem rather uninformative. It is the task of chemists to flesh out the meaning of these terms. If only ‘\(\mathrm{p}-\mathrm{V}\)’ work is involved,
\[\mathrm{w}=-\mathrm{p} \, \mathrm{dV} \label{d} \]
The point of Equation \ref{c} is to separate the work term from the heat term. The significance for chemists is that \(\mathrm{q}\) links to the Second Law of Thermodynamics. Thus chemists know that heat flows spontaneously from high to low temperatures. This concept of ‘spontaneous change’ is picked up with enormous impact in the second law.
Footnotes
[1] Peter Atkins (Galileo’s Finger, Oxford University press, 2003, page 107) speculates that the total energy of the universe ‘may be exactly zero’.
[2] In principle it is possible to calculate the total energy of a given system using a scale in conjunction with Einstein’s famous equation, \(\mathrm{E}=\mathrm{m} \, \mathrm{c}^{2}\). However the mass corresponding to \(1 \mathrm{~kJ}\) is only about \(10^{-14} \mathrm{~kg}\).