Abstract
The First and the Second Laws of Thermodynamics are presented. Their combination leads to the conclusion that one of the thermodynamic potentials, such as the energy or the free energy, becomes minimum when thermodynamic equilibrium is reached. Which one of them is minimized at equilibrium is determined by the boundary conditions. The important concept of chemical potential is introduced.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsNotes
- 1.
More accurately, U is the so-called internal energy, which is defined as the average value of the total energy E t of the system, under conditions of the total momentum being equal to zero on the average. (For macroscopic systems, the total angular momentum must be zero on the average as well). Notice that the value of U or E t is fully determined only after we choose a reference state, the energy of which is by definition zero. Usually, the reference state is the one at which all the particles of the system are at infinite distance from each other and at their ground state. There are three types of contributions to U or to E t : The rest relativistic energy \( E_{o} = \sum {m_{oi} } c^{2} \), the kinetic energy E K , and the potential energy E P , which may include interactions both with the environment and among the particles of the system itself. For convenience, it is not uncommon to ignore the rest energy by incorporating it in the reference state, if no changes in it are involved.
- 2.
These inequalities are: \( T \ge 0, C_{V} > 0, C_{P} > \,C_{V} , \left( {\partial P/\partial V} \right)_{T} < 0 \).
- 3.
A simple system, such as a perfect gas, when in equilibrium, can be described macroscopically by only three independent macroscopic variables U, V, N; for a photon system in equilibrium N is not an independent variable and, hence, only two independent variables are sufficient for its macroscopic description (see p. 35). Other more complicated systems in equilibrium may require a larger number of independent macroscopic variables. Non-equilibrium states of a system require more independent macroscopic variables than the ones required for the equilibrium state of the same system.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2011 Eleftherios N. Economou
About this chapter
Cite this chapter
Economou, E.N. (2011). Equilibrium and Minimization of Total Energy. In: A Short Journey from Quarks to the Universe. SpringerBriefs in Physics, vol 1. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-20089-2_4
Download citation
DOI: https://doi.org/10.1007/978-3-642-20089-2_4
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-20088-5
Online ISBN: 978-3-642-20089-2
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)