List of Physics Thermodynamics Formulas, Equations Latex Code

0

0

List of Physics Thermodynamics Formulas, Equations Latex Code

Navigation

In this blog, we will introduce most popuplar formulas in thermodynamics, Physics. We will also provide latex code of the equations. Topics include thermodynamics, heat capacity, conservation of energy, nernst's law, maxwell relations, adiabatic processes, isobaric processes, throttle processes, The Carnot Cycle, phase transitions, thermodynamic potential, ideal mixtures, thermodynamics statistical basis, etc.

• 1. Thermodynamics
• Thermodynamics Definitions
• Thermal Heat Capacity
• Thermodynamics Conservation of Energy
• Thermodynamics Nernst's law
• State functions Maxwell relations
• Reversible Adiabatic Processes
• Isobaric Processes
• Throttle Processes
• The Carnot Cycle
• Phase Transitions
• Thermodynamic Potential
• Ideal Mixtures
• Thermodynamics Statistical Basis

1. Thermodynamics

• Thermodynamics Definitions

  Equation

  
  
  

  Latex Code

              f(x,y,z)=0 \\
              dz=\left(\frac{\partial z}{\partial x}\right)_{y}dx+\left(\frac{\partial z}{\partial y}\right)_{x}dy \\
              \left(\frac{\partial x}{\partial y}\right)_{z}\cdot\left(\frac{\partial y}{\partial z}\right)_{x}\cdot\left(\frac{\partial z}{\partial x}\right)_{y}=-1 \\
              \varepsilon^m F(x,y,z)=F(\varepsilon x,\varepsilon y,\varepsilon z) \\
              mF(x,y,z)=x\frac{\partial F}{\partial x}+y\frac{\partial F}{\partial y}+z\frac{\partial F}{\partial z}
          

  Explanation

  Latex code for the Thermodynamics Introduction. I will briefly introduce the notations in this formulation.

  • : The total differential dz
  • A homogeneous function of degree m
  • : The isochoric pressure coefficient
  • : The isothermal compressibility
  • : The isobaric volume coefficient
  • : The adiabatic compressibility
  • : The ideal gas follows
  
  

  Related Documents

  • Physics Formulary

  Related Videos

• Thermal Heat Capacity

  Equation

  
  
  

  Latex Code

              C_p-C_V=T\left(\frac{\partial p}{\partial T}\right)_{V}\cdot\left(\frac{\partial V}{\partial T}\right)_{p}=-T\left(\frac{\partial V}{\partial T}\right)_{p}^2\left(\frac{\partial p}{\partial V}\right)_{T}\geq0 \\
              \displaystyle C_X=T\left(\frac{\partial S}{\partial T}\right)_{X} \\
              \displaystyle C_p=\left(\frac{\partial H}{\partial T}\right)_{p} \\
              \displaystyle C_V=\left(\frac{\partial U}{\partial T}\right)_{V} \\
              C_{mp}-C_{mV}=R
          

  Explanation

  Latex code for the Thermodynamics Introduction. I will briefly introduce the notations in this formulation.

  • : The specific heat at constant at X
  • : The specific heat at constant pressure
  • : The specific heat at constant volume
  
  

  Related Documents

  • Physics Formulary

  Related Videos

• Conservation of Energy

  Equation

  
  
  

  Latex Code

              Q=\Delta U+W \\
              d\hspace{-1ex}\rule[1.25ex]{2mm}{0.4pt} Q=dU+d\hspace{-1ex}\rule[1.25ex]{2mm}{0.4pt}W \\
              d\hspace{-1ex}\rule[1.25ex]{2mm}{0.4pt}W=pdV \\
              Q=\Delta H+W_{\rm i}+\Delta E_{\rm kin}+\Delta E_{\rm pot}
          

  Explanation

  Latex code for the Thermodynamics Introduction. I will briefly introduce the notations in this formulation.

  • : The total added heat
  • : The work done
  • : The difference in the internal energy
  
  

  Related Documents

  • Physics Formulary

  Related Videos

• Thermodynamics Nernst's law

  Equation

  
  
  

  Latex Code

              \lim_{T\rightarrow0}\left(\frac{\partial S}{\partial X}\right)_{T}=0
          

  Explanation

  Latex code for the Thermodynamics Nernst's law. I will briefly introduce the notations in this formulation. Absolute zero temperature cannot be reached by cooling through a finite number of steps.

  • : The total added heat
  • : The work done
  • : The difference in the internal energy
  
  

  Related Documents

  • Physics Formulary

  Related Videos

• State functions Maxwell Relations

  Equation

  
  
  

  Latex Code

              \left(\frac{\partial T}{\partial V}\right)_{S}=-\left(\frac{\partial p}{\partial S}\right)_{V}~,~~\left(\frac{\partial T}{\partial p}\right)_{S}=\left(\frac{\partial V}{\partial S}\right)_{p}~,~~ \left(\frac{\partial p}{\partial T}\right)_{V}=\left(\frac{\partial S}{\partial V}\right)_{T}~,~~\left(\frac{\partial V}{\partial T}\right)_{p}=-\left(\frac{\partial S}{\partial p}\right)_{T} \\
              TdS=C_VdT+T\left(\frac{\partial p}{\partial T}\right)_{V}dV~~\mbox{and}~~TdS=C_pdT-T\left(\frac{\partial V}{\partial T}\right)_{p}dp
  
          

  Explanation

  Latex code for the State functions Maxwell Relations. I will briefly introduce the notations in this formulation. Absolute zero temperature cannot be reached by cooling through a finite number of steps.

  • : Internal energy,
  • : Enthalpy ,
  • : Free energy,
  • : Gibbs free energy,
  
  

  Related Documents

  • Physics Formulary

  Related Videos

• Reversible Adiabatic Processes

  Equation

  
  
  

  Latex Code

              \text{adiabatic processes} \\
              W=U_1-U_2 \\
              \text{reversible adiabatic processes} \\
              \gamma=C_p/C_V
          

  Explanation

  Latex code for the Reversible Adiabatic Processes. I will briefly introduce the notations in this formulation.

  
  

  Related Documents

  • Physics Formulary

  Related Videos

• Isobaric Processes

  Equation

  
  
  

  Latex Code

              \text{Isobaric Processes} \\
              H_2-H_1=\int_1^2 C_pdT \\
              \text{Reversible isobaric process} \\
              H_2-H_1=Q_{\rm rev}
          

  Explanation

  Latex code for the Isobaric Processes. I will briefly introduce the notations in this formulation.

  
  

  Related Documents

  • Physics Formulary

  Related Videos

• Throttle Processes

  Equation

  
  
  

  Latex Code

              \alpha_H=\left(\frac{\partial T}{\partial p}\right)_{H}=\frac{1}{C_p}\left[T\left(\frac{\partial V}{\partial T}\right)_{p}-V\right]
          

  Explanation

  Latex code for the Throttle Processes. The throttle process is used in refrigerators for example. I will briefly introduce the notations in this formulation.

  • : conserved quantity
  
  

  Related Documents

  • Physics Formulary

  Related Videos

• The Carnot Cycle

  Equation

  
  
  

  Latex Code

              \eta=1-\frac{|Q_2|}{|Q_1|}=1-\frac{T_2}{T_1}:=\eta_{\rm C} \\
              \xi=\frac{|Q_2|}{W}=\frac{|Q_2|}{|Q_1|-|Q_2|}=\frac{T_2}{T_1-T_2}
          

  Explanation

  Latex code for the Carnot Cycle. The throttle process is used in refrigerators for example. I will briefly introduce the notations in this formulation.

  • : efficiency for a Carnot cycle
  • : the cold factor when process is applied in reverse order and the system performs a work -W
  
  

  Related Documents

  • Physics Formulary

  Related Videos

• Phase Transitions

  Equation

  
  
  

  Latex Code

              \Delta S_m=S_m^\alpha - S_m^\beta=\frac{r_{\beta\alpha}}{T_0} \\
              S_m=\left(\frac{\partial G_m}{\partial T}\right)_{p} \\
              \frac{dp}{dT}=\frac{S_m^\alpha-S_m^\beta}{V_m^\alpha-V_m^\beta}= \frac{r_{\beta\alpha}}{(V_m^\alpha-V_m^\beta)T} \\
              p=p_0{\rm e}^{-r_{\beta\alpha/RT}} \\
              r_{\beta\alpha}=r_{\alpha\beta} \\
              r_{\beta\alpha}=r_{\gamma\alpha}-r_{\gamma\beta} \\
              \frac{dp}{dT}=\frac{S_m^\alpha-S_m^\beta}{V_m^\alpha-V_m^\beta}= \frac{r_{\beta\alpha}}{(V_m^\alpha-V_m^\beta)T} \\
              p=p_0{\rm e}^{-r_{\beta\alpha/RT}}
          

  Explanation

  Latex code for the Carnot Cycle. Phase transitions are isothermal and isobaric. I will briefly introduce the notations in this formulation.

  • : ideal gas one finds for the vapor line at some distance from the critical point.
  
  

  Related Documents

  • Physics Formulary

  Related Videos

• Thermodynamic Potential

  Equation

  
  
  

  Latex Code

              dG=-SdT+Vdp+\sum_i\mu_idn_i \\
              \displaystyle\mu=\left(\frac{\partial G}{\partial n_i}\right)_{p,T,n_j} \\
              V=\sum_{i=1}^c n_i\left(\frac{\partial V}{\partial n_i}\right)_{n_j,p,T}:=\sum_{i=1}^c n_i V_i \\
              \begin{aligned} V_m&=&\sum_i x_i V_i\\ 0&=&\sum_i x_i dV_i\end{aligned}
          

  Explanation

  Latex code for the Thermodynamic Potential. I will briefly introduce the notations in this formulation.

  • : thermodynamic potential.
  • : partial volume of component i.
  
  

  Related Documents

  • Physics Formulary

  Related Videos

• Ideal Mixtures

  Equation

  
  
  

  Latex Code

              U_{\rm mixture}=\sum_i n_i U^0_i \\ 
              H_{\rm mixture}=\sum_i n_i H^0_i \\ 
              S_{\rm mixture}=n\sum_i x_i S^0_i+\Delta S_{\rm mix} \\
              \Delta S_{\rm mix}=-nR\sum\limits_i x_i\ln(x_i)
          

  Explanation

  Latex code for the Ideal Mixtures. I will briefly introduce the notations in this formulation.

  • : one component in a second gives rise to an increase in the boiling point
  • : one component in a second gives rise to decrease of the freezing point
  
  

  Related Documents

  • Physics Formulary

  Related Videos

• Thermodynamics Statistical Basis

  Equation

  
  
  

  Latex Code

              P=N!\prod_i\frac{g_i^{n_i}}{n_i!} \\
              n_i=\frac{N}{Z}g_i\exp\left(-\frac{W_i}{kT}\right) \\
              Z=\sum\limits_ig_i\exp(-W_i/kT) \\
              Z=\frac{V(2\pi mkT)^{3/2}}{h^3} \\
              \text{Entropy in Thermodynamic Equilibrium} \\
              S=\frac{U}{T}+kN\ln\left(\frac{Z}{N}\right)+kN\approx\frac{U}{T}+k\ln\left(\frac{Z^N}{N!}\right) \\
              \text{Ideal gas} \\
              S=kN+kN\ln\left(\frac{V(2\pi mkT)^{3/2}}{Nh^3}\right)
          

  Explanation

  Latex code for the Thermodynamics Statistical Basis. I will briefly introduce the notations in this formulation.

  • : number of possibilities
  • : number of particles
  • : number of possible energy levels
  • : g-fold degeneracy
  • : The occupation numbers in equilibrium(with the maximum value for P)
  • : State sum Z is a normalization constant
  • : one component in a second gives rise to decrease of the freezing point
  
  

  Related Documents

  • Physics Formulary

  Related Videos