Physics Formulae/Thermodynamics Formulae

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

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

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

Ideal Gas Law  




Translational Energy  
Internal Energy  

Thermal Transitions edit



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

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


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


Entropic Force  

Thermal Transfer edit

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

Engine Efficiency  
Carnot Engine Efficiency  
Refrigeration Performance  
Carnot Refrigeration Performance