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

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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

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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

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Ideal Gas Law  

 

 


 

Translational Energy  
Internal Energy  


Thermal Transitions

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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

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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

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


Thermal Efficiencies

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Engine Efficiency  
Carnot Engine Efficiency  
Refrigeration Performance  
Carnot Refrigeration Performance