3. Glossary of Terms and Variables
3.1. Glossary of Terms
Adiabatic: Without the transfer of heat; \(q=0\) for an adiabatic process. Consider the specific example of a reaction performed in a container that is surrounded by styrofoam that does not conduct heat.
Bond Dissociation Enthalpy: The standard enthalpy change for breaking a chemical bond. It can be thought of as the amount of work required to pull apart two atoms.
Chemical Potential (also known as partial molar Gibbs free energy)
Closed System: A system which cannot exchange matter with the surroundings.
Colligative Properties: Properties of a solution whose effects depend on mole fraction of a dissolved species rather than the nature of the solute. Example colligative properties include Raoult’s law, osmotic pressure, freezing point depression, and boiling point elevation.
Diathermal: Allowing the transfer of heat.
Differential
Energy: The capacity for doing work.
Endothermic Process: A process in which the system absorbs heat, where \(q>0\).
Enthalpy: A state function defined as \(H=U+PV\) that describes the energy of a system. This definition is convenenient since for a process at constant pressure, the change in enthalpy is equal to heat transferred, or \(\Delta H = q_p\).
Entropy:
Equation of State: A mathematical expression which describes the properties of a system, typically using just a few variables or paramteters. For instance the ideal gas equation or the van der Waals equations are very well known equations of state.
Equipartition of energy theorem
Exact
Exothermic Process: A process in which the system releases heat, where \(q<0\).
Extensive Variable: A variable whose value depends on the size of the system such as \(n\) or \(V\).
First Law of Thermodynamics: Internal energy is a state function and is given by \(\Delta U = q + w\).
Gibbs Free Energy: A state function defined as \(G=H-TS\). At constant pressure and temperature, a change in Gibbs free energy for a spontaneous process describes the maximum amount of non-pressure-volume work that can be obtained from the system.
Heat: Thermal energy which flows from a hotter object to a colder one.
Heat Engine: A heat engine is a device which uses a cyclic process to convert thermal energy into mechanical work.
Helmholtz Free Energy: A state function defined as \(A=U-TS\). At constant volume and temperature, a change in Helmholtz free energy for a spontaneous process describes the maximum amount of non-pressure-volume work that can be obtained from the system.
Ideal Gas: An ideal gas consists of infinitesimal point-like particles that have mass, that do not interact with each other, and that collide elastically (with no loss of energy) with container wall. The equation of state for an ideal gas is \(PV=nRT\).
Ideal solution: An ideal solution consists of a solute dissolved in a solvent where the intermolecular forces are the same for solvent-solvent, solvent-solute, and solute-solute interactions. An ideal solution obeys the equation \(\mu_i(\textrm{solution}) = \mu_i^*(\textrm{liquid}) + RT\ln x_i\).
Inexact
Intensive Variable: A variable whose value is independent of the size of the system such as \(P\) or \(T\).
Internal Energy: A state function that describes the energy contained within a system relative to a standard state.
Intensive reaction rate
Irreversible
Isolated System: A system which cannot exchange matter, work, or heat with the surroundings.
Open System: A system which can exchange matter or energy with the surroundings.
Osmotic Pressure: The pressure applied to a solution that stops the inward flow of pure solvent across a semipermeable membrane.
Path function
Phase: A sample of matter that has uniform chemical and physical properties.
Reaction order
Reversible
Second Law of Thermodynamics: Entropy is a state function and can be calculated using \(dS=dq/T\) for a reversible path; the entropy change of the universe is zero for a reversible process and positive for an irreversible (spontaneous) process.
Standard state
State function
Surroundings:
System: The part of the universe under consideration for analysis.
Temperature: A measure of hotness or coldness. This is an intuitive definition; a more rigorous definition of requires a discussion of statistical mechanics which is beyond the scope of this material. Modern temperature scales are defined by two points including absolute zero and the triple point of water.
Thermodynamic Equilibrium: A state of a system where \(T\), \(P\), \(V\), etc., are unchanging and there is no more potential for change.
Third Law of Thermodynamics: The entropy of a pure, perfect crystalline solid at 0 K is 0 J/K.
van der Waals Gas Equation of State: A minimal model for a real gas (\(P=\frac{nRT}{V-nb}-a\frac{n^2}{V^2}\)) that accounts for intermolecular interactions (with the \(a\) term) and excluded volume (with the \(b\) term) and where these terms are in general different for different gases.
Vapor pressure: The pressure of a vapor in equilibrium with a solid or liquid.
Work: Mechanical work is force times distance (most generally written as \(w = \int Fdx\)) or pressure times change in volume (\(w = -\int PdV\)). Note the sign convention for pressure-volume work. Non-pressure-volume work may also bew considered at times depending on the situation, such as work done when moving a charged particle \(Q\) through an electric field (\(w=\int QEdx\)) or for electrical work (\(w=\int Pdt\), where \(P\) is power here).
Zeroth Law of Thermodynamics: Two objects that are each in thermal equilibrium with a third object are also in thermal equilibrium with each other. This establishes that temperature is the property that determines whether two objects in thermal contact are in thermal equilibrium with each.
3.2. List of Variables, Constants, and Symbols
SI units are preferred in general and often help to avoid unit conversion errors. SI units are listed below, in most cases; unitless quantities are left blank in the units column.
Symbol or Abbreviation |
Name |
Units or Value |
|---|---|---|
\(a\) |
acceleration |
\(\dfrac{\textrm{m}}{\textrm{s}^2}\) |
\(A\) |
area |
\(\textrm{m}^2\) |
\(C\) |
specific heat capacity |
\(\dfrac{\textrm{J}}{\textrm{K g}}\) |
\(\overline{C}\) |
molar heat capacity |
\(\dfrac{\textrm{J}}{\textrm{K mol}}\) |
\(\overline{C}_\textrm{P}\) |
constant pressure molar heat capacity |
\(\dfrac{\textrm{J}}{\textrm{K mol}}\) |
\(\overline{C}_\textrm{V}\) |
constant volume molar heat capacity |
\(\dfrac{\textrm{J}}{\textrm{K mol}}\) |
\(\textrm{d}\) |
infinitesimal change (for derivative) |
|
\(\partial\) |
infinitesimal change (for partial derivative) |
|
\(\Delta\) |
discrete change |
|
\(\varepsilon\) |
kinetic energy |
\(\textrm{J}\) |
\(F\) |
force |
\(\textrm{N}\), \(\dfrac{\textrm{kg m}}{\textrm{s}^2}\) |
\(\gamma\) |
reaction order |
unitless |
\(G\) |
Gibbs free energy |
\(\textrm{J}\) or \(\textrm{J/mol}\) |
\(\Delta G^\circ\) |
standard Gibbs free energy change |
\(\textrm{J}\) or \(\textrm{J/mol}\) |
\(k\) |
reaction rate constant |
variable (depends on sum of reaction orders) |
\(k_\textrm{B}\) |
Boltzmann’s constant (\(1.381\times10^{-23} J/K)\) |
\(\textrm{J/K}\), equal to \(R/N_\textrm{A}\) |
\(H\) |
enthalpy |
\(\textrm{J}\) or \(\textrm{J/mol}\) |
\(\Delta_f H^\circ\) |
enthalpy of formation |
\(\textrm{J/mol}\) |
\(\Delta H^\circ_\textrm{fus}\) |
enthalpy of fusion |
\(\textrm{J/mol}\) |
\(\Delta H^\circ_\textrm{vap}\) |
enthalpy of vaporization |
\(\textrm{J/mol}\) |
\(\Delta H^\circ\) |
standard enthalpy change |
\(\textrm{J}\) or \(\textrm{J/mol}\) |
\(K\) |
equilibrium constant |
unitless |
\(K_\textrm{d}\) |
dissociation constant |
\(\textrm{M}\) |
\(K_\textrm{a}\) |
association constant |
\(\textrm{1/M}\) |
\(L\) |
length |
\(\textrm{m}\) |
\(m\) |
mass |
\(\textrm{kg} = 1000 \textrm{ g}\) |
\(M\) |
molar mass |
\(\textrm{g/mol}\) (non-SI unit) |
\(n\) |
moles |
1 mol = \(6.022\times10^{23}\) |
\(\nu\) |
stoichiometric coefficient |
unitless (products positive, reactants negative) |
\(N\) |
number of particles |
unitless |
\(N_\textrm{A}\) |
Avogadro’s number |
\(N_\textrm{A}=6.022\times10^{23}/\textrm{mol}\) |
\(p\) |
momentum |
\(\textrm{kg m/s}\) |
\(P\) |
pressure |
\(\textrm{Pa}\) or \(\textrm{atm}\), where \(\textrm{Pa} = \dfrac{\textrm{N}}{\textrm{m}^2}\) and \(1\textrm{ atm} = 101325 \textrm{ Pa}\) |
\(q\) |
heat (positive sign if added to system) |
\(\textrm{J}\) |
\(q_\textrm{P}\) |
heat for a constant pressure process |
\(\textrm{J}\) |
\(\textrm{R}\) |
gas constant (8.314 J/K*mol) |
\(\dfrac{\textrm{J}}{\textrm{K mol}}\) |
\(R\) |
reaction rate |
\(\textrm{M/s}\) |
RMS |
root-mean-square |
|
\(T\) |
temperature |
\(\textrm{K}\) or °\(\textrm{C}\) |
\(v\) |
speed |
\(\textrm{m/s}\) |
\(U\) |
internal energy |
\(\textrm{J}\) or \(\textrm{J/mol}\) |
\(V\) |
volume |
\(\textrm{m}^3 = 1000 \textrm{ L} = 10^6 \textrm{ cm}^3\) |
\(w\) |
work (\(PV\) work sign positive for compression) |
\(\textrm{J}\) |
\(\xi\) |
extent of reaction |
\(\textrm{moles}\) |