THERMAL PHYSICS AND MATERIALS
GLOSSARY OF TERMS
Absolute (Kelvin) temperature scaleis basedon fixing T of the triple pointfor water (a specific T = 273.16 K and P = 611.73 Pa where water can coexist inthe solid, liquid, and gasphases in equilibrium).
Adiabatic is a thermodynamic process in which no heat is transferred to or from the working fluid
Avogadro’s law At constant T and p, equal volumes of gases contain equal numbers of atoms, molecules (entities).Avogrado’s constant
Boltzmann factor (Pi) The e(-E/kT) factor in Maxwell Boltzmann distribution.
Bose-Einstein Distributionbosons with the same energy can occupy the same state
Bosonselementary particle with integer spin
Boyle Temperature, TB : The temperature at which z = 1 and B = 0 . Boyle Line : The p (T) line for z =1. At its Boyle temperature, T = TB, a gas behaves more like a perfect (ideal) gas than at any other temperature / shows its most ideal behaviour over the largest range of pressures.
Chemical Potential 1: As a function of position, the chemical potential measures the tendency of particles to diffuse. 2: When a reaction may occur, an extremum of some thermodynamic function determines equilibrium. The chemical potential measures the contribution (per particle and for an individual species) to the function’s rate of change. 3: The chemical potential provides a characteristic energy: (∂E/∂N)S,V, that is, the change in energy when one particle is added to the system at constant entropy and volume.
Clausius-Clapeyron Equation.An equation which relates the vapor pressure at certain temperatures to the heat of vaporization.
Closed systems exchange energy but not matter with the environment.
Condensation nuclei are airborne particles (aerosols) composed of soluble salts such as ammonium sulphate or sea-salt. These nuclei, due to their affinity for water, are hygroscopic.
Critical point, also called a critical state, specifies the conditions (temperature, pressure and sometimes composition) at which a phase boundary ceases to exist
Critical Radiusthe minimum size that must be formed before a droplet is stable and begins to grow
Enthalpy (H)is a measure of the total energy of a thermodynamic system. It includes the internal energy, which is the energy required to create a system, and the amount of energy required to make room for it by displacing its environment and establishing its volume and pressureH = H (p,T) = U + pV
Entropy (S) is a thermodynamic property that is a measure of the energy not available for useful work in a thermodynamic process, such as in energy conversion devices, engines, or machines. Such devices can only be driven by convertible energy, and have a theoretical maximum efficiency when converting energy to work. During this work entropy accumulates in the system, but has to be removed by dissipation in the form of waste heat
Equation of StatepV = nRT
Equilibriumis characterized by a minimum in Free Energy and maximum Entropy.
Equipartition theorem. Molecules in thermal equilibrium have the same average energy associated with each independent degree of freedom of their motion.
General formula that relates the temperature of a system with its average energies. The equipartition theorem is also known as the law of equipartition, equipartition of energy, or simply equipartition. The original idea of equipartition was that, in thermal equilibrium, energy is shared equally among all of its various forms; for example, the average kinetic energy per degree of freedom in the translational motion of a molecule should equal that of its rotational motions.
Extensive properties, e.g., mass, mole number, volume (additive, e.g., when two systems are combined; measured directly)
Fermi-Dirac Distributionno two fermions can occupy the same state
Fermionselementary particlewith half-integer spin
First Law (Conservation of energy).For a thermodynamic system a new state function can be defined, the “internal energy” U (dimension of energy: Joule) representing an extension to mechanical energy.This thermodynamic energy is conserved in an isolated system which does not exchange heat, work, or matter with its environment, i.e., U remains constant during all (reversible) changes of the system under such conditions.dE = ∂w + ∂Q
For quantum mechanical reasons, some of these degrees of freedom may not be available, or only partially available to store thermal energy, at a given temperature. As the temperature approaches absolute zero, the specific heat capacity of a system also approaches zero, due to loss of available degrees of freedom due to the quantum mechanical effect. Quantum theory can be used to quantitatively predict specific heat capacities in simple systems.
Free Energy and entropy“Free Energy” means the maximum fraction of the total energy contained in a system which is available to perform work on the surroundings. Entropy is a measure of energy NOT available to perform work.
Fugacity (f) of a real gas is an effective pressure which replaces the true mechanical pressure in accurate chemical equilibrium calculations. It is equal to the pressure of an ideal gas which has the same chemical potential as the real gas. For example, nitrogen gas (N2) at 0°C and a pressure of 100 atm has a fugacity of 97.03 atmThis means that the chemical potential of real nitrogen at a pressure of 100 atm has the value which ideal nitrogen would have at a pressure of 97.03 atm.
Gibbs free energy(G) also known as free enthalpy to distinguish it from Helmholtz free energy is a thermodynamic potential that measures the "useful" or process-initiating work obtainable from an isothermal, isobaric thermodynamic system.
Gibbs’ phase rulewhere P is the number of phases in thermodynamic equilibrium with each other and C is the number of components. Typical phases are solids, liquids and gases. A system involving one pure chemical is an example of a one-component system. Two-component systems, such as mixtures of water and ethanol, have two chemically independent components. F is the number of degrees of freedom, which means the number of intensive properties such as temperature or pressure, which are independent of other intensive variables. This version of the Gibbs' phase rule is only valid for non-reacting systems.
D = C – P + 2
Guggenheim scheme
+dSU dV -
H F
+dpG dT –
dU = T dS - p dV
dH = T dS + V dp
dF = - S dT - p dV
dG = - S dT + V dp
Heat capacity the amount of heat required to change a body's temperature by a given amount Cv
Helmholtz free energy (F)is a thermodynamic potential which measures the “useful” work obtainable from a closed thermodynamic system at a constant temperature and volume. For such a system, the negative of the difference in the Helmholtz energy is equal to the maximum amount of work extractable from a thermodynamic process in which temperature and volume are held constant. Under these conditions, it is minimized at equilibrium
Hydrogen bonding When a Hydrogen atom bonds with an electronegative atom, its electron cloud is mostly around the electronegative atom leaving the Hydrogen looking positively charged. This can attract another atom for bonding.
Hydrostatic Eqnμ(p) + M g z = const.
Ideal Gas Ideal gas law fixed amount of gas pV/T = const Ideal gas law variable amount of gas pV/T = R = 8.314 J K-1mol-1
Includes dipole-dipole, dipole-induced dipole, and London forces (transitory forces, dipole induced in atoms, molecules which are, on average, neutral.
Intensive Properties, e.g., pressure, temperature, density, mole fraction, refractive index... (non-additive, locally defined, measured „statistically“)
Isolated systems can exchange neither energy nor matter with the environment.
Joule Thompson co-efficient The rate of change of temperature T with respect to pressure P in a Joule–Thomson process (that is, at constant enthalpy H) is the Joule–Thomson (Kelvin) coefficientμJT
Kelvin Equation The Kelvin Equation demonstrates that at any given temperature the saturation vapour pressure over the surface of a water drop is larger than that over a flat surface, and increasingly so with decreasing radius. Accordingly, in the atmosphere large drops grow by vapour diffusion at the expense of the smaller ones.
Law of Corresponding States All fluids, when compared at the same reduced temperature and reduced pressure, have approximately the same compressibility factor and all deviate from ideal gas behavior to about the same degree.
Law of corresponding statesAll fluids, when compared at the same reduced temperature and reduced pressure, have approximately the same compressibility factor and all deviate from ideal gas behavior to about the same degree.
Lennard Jones potential (also referred to as the L-J potential, 6-12 potential, or 12-6) is a mathematically simple model that approximates the interaction between a pair of neutral atoms or molecules
Mean free path λ : average distance a molecule travels before colliding with another molecule (d = effective diameter of a molecule)
Mixture : A phase with uniform chemical composition is called a pure phase, otherwise it is called a mixture.
Molar heat capacity Heat capacity per mole cv
NA= total number of entities (atoms, molecules, electrons,…) per mole = 6.022 x 1023/mol
Open systems can exchange both matter and energy with the environment.
Partial PressureIn a mixture of ideal gases, each gas has a partial pressure which is the pressure which the gas would have if it alone occupied the volume. The total pressure of a gas mixture is the sum of the partial pressures of each individual gas in the mixture.
Partition function (Z) Sum of the Boltzmann factors
Phase : A body which is homogeneous in its intensive properties (e.g., p, density, refractive index)
Raoult’s Law Adding a solute to a pure liquid, the solute "seeks to spread over the most possible” volume in the liquid (entropy increase). This requires additional (liquid) space which can only be achieved by additional condensation of gas, thus reducing the number of gas molecules, i.e., the gas pressure above the liquid (energy reduction).
Ratio of Heat Capacitiescp / cv= (cv + R) / cv = γ (Poisson exponent)
Reduced variablesThe ratio of the temperature of a substance to its critical temperature. The ratio of the pressure of a substance to its critical pressure
Relative humiditythe partial pressure of water vapour in air-water mixture given as a percentage of the saturated vapour pressure (under the same conditions)
Reversible Heatis defined in general asδQ = dE – δA
Schwarz rule If the taking the partial derivatives of a function, say F(x,y), are such that Fxy= Fyx
Second Law All work can be converted completely to heat. However, heat cannot be completely and continuously converted into work. ∂S >= 0
Solution : A mixture with one dominant substance (solvent); solvent, solute
Specific heat capacity (const. volume) approaches zero at zero kelvin.Cv-> 0
Specific heatcapacity (specific heat) Heat capacity per unit mass cv*
State function If the function satisfies Schwarz rule Fxy=FyxIt is independent of the path taken (E.g. gravity). Whereas work done is path dependant so is not a state function
Supercritical fluid is any substance at a temperature and pressure above its critical point, where distinct liquid and gas phases do not exist. It can effuse through solids like a gas, and dissolve materials like a liquid. In addition, close to the critical point, small changes in pressure or temperature result in large changes in density, allowing many properties of a supercritical fluid to be "fine-tuned". Supercritical fluids are suitable as a substitute for organic solvents in a range of industrial and laboratory processes. Carbon dioxide and water are the most commonly used supercritical fluids, being used for decaffeination and power generation, respectively.
The State of Thermodynamic Equilibrium No matter what is the initial state of an isolated system, eventually it will reach the State of Thermodynamic Equilibrium(no macroscopic processes, only microscopic motion of molecules).
Triple point In thermodynamics, the triple point of a substance is the temperature and pressure at which three phases (for example, gas, liquid, and solid) of that substance coexist in thermodynamic equilibrium. Defined as 273.16K.
Van der Waals equation (p2 + a/v2)(v-b) = RT
Van der Wall cohesion pressure PidealPreal
Van der Wall covolumevidealvreal
Van der Wall forces A force acting between non-bonded atoms or molecules.
Vapour pressure. Is the pressure of a vapor in thermodynamic equilibrium with its condensed phases in a closed system. All liquids have a tendency to evaporate, and some solids can sublime into a gaseous form. Vice versa, all gases have a tendency to condense back to their liquid form, or deposit back to solid form.The equilibrium vapor pressure is an indication of a liquid's evaporation rate. It relates to the tendency of particles to escape from the liquid (or a solid). A substance with a high vapor pressure at normal temperatures is often referred to as volatile
Water vapour saturation(S) =100% rH
Work required to change an extensive property can be defined as a sum of products between extensive (Yi) and intensive (zi) properties. Reversible Work δA = ΣzidYiIn case of volume (V) this is pressure (p) with the product (pdV) having the dimension of work (Nm = Ws = J). In case of surface work: surface tension (σ) times surface (Ω)change (σdΩ).Sign ConventionVolume work δA = –p dV has a negative sign.Thus, work done onthe system by reducing V, (dV<0), is positive, work done bythe system (expansion) is negative.
Work∂W= P (x,y) dx + Q(x,y) dywhere P, Q are the components of a Force FP = Wx = Fx and Q = Wy = Fy W is not a state function.
Zeroth Law When two systems A and B are each in thermal equilibrium with a third system C then they are also in thermal equilibrium with each other.
ABBREVIATIONS
CN = Condensation Nuclei
Cp = Heat Capacity (at constant pressure)
Cv = Heat Capacity (at constant volume)
E = energy
e = p
es= psat
f = fugacity
F = Helmholtz Free Energy
G = Gibbs Free Energy(or Free Enthalpy)
H = enthalpy
kB= Boltzmann’s constant
M = molar mass
n = mole number
p = pressure
P = probability
p∞= saturationvapour pressure at “infinite” radius
pg= water vapour pressure
pw= vapour pressure inside the droplet (at the liquid / gas boundary)
Q = Heat
Rc= critical radius
rH= Relative Humidity
S = Entropy
S = Saturation Ratio
T = temperature
TB= Boyle temp.
U = internal energy
v = molar volume
V = volume
W = reversible work
Yi = Extensive properties
Z = partition function
zi = intensive properties
α = expansion coeff
β = tension coeff
γ = compressibility factor
γ =Poisson exponent
εF =Fermi energy
η = Thermal Efficiency
λ = Mean free path
μi =Chemical Potential
σ = surface tension
Ω = surface area