Physics Formulae/Thermodynamics Formulae

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Lead Article: Tables of Physics Formulae


This article is a summary of the laws, principles, defining quantities, and useful formulae in the analysis of Thermodynamics.


Thermodynamics Laws[edit | edit source]

Zeroth Law of Thermodynamics

(systems in thermal equilibrium)

First Law of Thermodynamics △Q = △U +△W


Internal energy increase , decrease

Heat energy transferred to system , from system

Work done transferred to system by system

Second Law of Thermodynamics
Third Law of Thermodynamics

Thermodynamic Quantities[edit | edit source]

Quantity (Common Name/s) (Common Symbol/s) Defining Equation SI Units Dimension
Number of Molecules dimensionless dimensionless
Temperature K [Θ]
Heat Energy J [M][L]2[T]-2
Latent Heat J [M][L]2[T]-2
Entropy J K-1 [M][L]2[T]-2 [Θ]-1
Heat Capacity (isobaric) J K -1 [M][L]2[T]-2 [Θ]-1
Specific Heat Capacity (isobaric) J kg-1 K-1 [L]2[T]-2 [Θ]-1
Molar Specific Heat

Capacity (isobaric)

J K -1 mol-1 [M][L]2[T]-2 [Θ]-1 [N]-1
Heat Capacity (isochoric) J K -1 [M][L]2[T]-2 [Θ]-1
Specific Heat Capacity (isochoric) J kg-1 K-1 [L]2[T]-2 [Θ]-1
Molar Specific Heat

Capacity (isochoric)

J K -1 mol-1 [M][L]2[T]-2 [Θ]-1 [N]-1
Internal Energy

Sum of all total energies which

constitute the system

J [M][L]2[T]-2
Enthalpy J [M][L]2[T]-2
Gibbs Free Energy J [M][L]2[T]-2
Helmholtz Free Energy J [M][L]2[T]-2
Specific Latent Heat J kg-1 [L]2[T]-2
Ratio of Isobaric to

Isochoric Heat Capacity,

Adiabatic Index

dimensionless dimensionless
Linear Coefficient of Thermal Expansion K-1 [Θ]-1
Volume Coefficient of Thermal Expansion K-1 [Θ]-1
Temperature Gradient No standard symbol K m-1 [Θ][L]-1
Thermal Conduction Rate/

Thermal Current

W = J s-1 [M] [L]2 [T]-2
Thermal Intensity W m-2 [M] [L]-1 [T]-2
Thermal Conductivity W m-1 K-1 [M] [L] [T]-2 [Θ]-1
Thermal Resistance m2 K W-1 [L] [T]2 [Θ]1 [M]-1
Emmisivity Coefficient Can only be found from experiment

for perfect reflector

for perfect absorber

(true black body)

dimensionless dimensionless


Kinetic Theory[edit | edit source]

Ideal Gas Law


Translational Energy
Internal Energy


Thermal Transitions[edit | edit source]

Adiabatic

Work by an Expanding Gas Process


Net Work Done in Cyclic Processes

Isobaric Transition
Cyclic Process
Work, Isochoric
work, Isobaric
Work, Isothermal
Adiabatic Expansion

Free Expansion


Statistical Physics[edit | edit source]

Below are useful results from the Maxell-Boltzmann distribution for an ideal gas, and the implications of the Entropy quantity.


Degrees of Freedom
Maxwell-Boltzmann Distribution,

Mean Speed

Maxwell-Boltzmann Distribution

Mode-Speed

Root Mean Square Speed
Mean Free Path ?
Maxwell–Boltzmann Distribution
Multiplicity of Configurations
Microstate in one half of the box
Boltzmann's Entropy Equation
Irreversibility
Entropy
Entropy Change

Entropic Force


Thermal Transfer[edit | edit source]

Stefan-Boltzmann Law
Net Intensity Emmision/Absorbtion
Internal Energy of a Substance
Work done by an Expanding Ideal Gas
Meyer's Equation


Thermal Efficiencies[edit | edit source]

Engine Efficiency
Carnot Engine Efficiency
Refrigeration Performance
Carnot Refrigeration Performance