Question

List of all important formula for thermodynamics

Answer 1

The equations in this article are classified by subject.

Phase transitionsEdit

Physical situationEquationsAdiabatic transition{\displaystyle \Delta Q=0,\quad \Delta U=-\Delta W\,\!}Isothermal transition{\displaystyle \Delta U=0,\quad \Delta W=\Delta Q\,\!}

For an ideal gas
{\displaystyle W=kTN\ln(V_{2}/V_{1})\,\!}

Isobaric transitionp1 = p2, p = constant

{\displaystyle \Delta W=p\Delta V,\quad \Delta q=\Delta U+p\delta V\,\!}

Isochoric transitionV1 = V2, V = constant

{\displaystyle \Delta W=0,\quad \Delta Q=\Delta U\,\!}

Adiabatic expansion{\displaystyle p_{1}V_{1}^{\gamma }=p_{2}V_{2}^{\gamma }\,\!}

{\displaystyle T_{1}V_{1}^{\gamma -1}=T_{2}V_{2}^{\gamma -1}\,\!}

Free expansion{\displaystyle \Delta U=0\,\!}Work done by an expanding gasProcess

{\displaystyle \Delta W=\int _{V_{1}}^{V_{2}}p\mathrm {d} V\,\!}

Net Work Done in Cyclic Processes
{\displaystyle \Delta W=\oint _{\mathrm {cycle} }p\mathrm {d} V\,\!}

Kinetic theoryEdit

Ideal gas equationsPhysical situationNomenclatureEquationsIdeal gas law

p = pressureV = volume of containerT = temperaturen = number of molesR = Gas constantN = number of moleculesk = Boltzmann's constant

{\displaystyle pV=nRT=kTN\,\!}

{\displaystyle {\frac {p_{1}V_{1}}{p_{2}V_{2}}}={\frac {n_{1}T_{1}}{n_{2}T_{2}}}={\frac {N_{1}T_{1}}{N_{2}T_{2}}}\,\!}

Pressure of an ideal gas

m = mass of one moleculeMm = molar mass

{\displaystyle p={\frac {Nm\langle v^{2}\rangle }{3V}}={\frac {nM_{m}\langle v^{2}\rangle }{3V}}={\frac {1}{3}}\rho \langle v^{2}\rangle \,\!}

Ideal gasEdit

QuantityGeneral EquationIsobaric
Δp = 0Isochoric
ΔV = 0Isothermal
ΔT = 0Adiabatic
{\displaystyle Q=0}Work
W{\displaystyle \delta W=-pdV\;}{\displaystyle -p\Delta V\;}{\displaystyle 0\;}{\displaystyle -nRT\ln {\frac {V_{2}}{V_{1}}}\;}

{\displaystyle -nRT\ln {\frac {P_{1}}{P_{2}}}\;}

{\displaystyle {\frac {PV^{\gamma }(V_{f}^{1-\gamma }-V_{i}^{1-\gamma })}{1-\gamma }}=C_{V}\left(T_{2}-T_{1}\right)}Heat Capacity
C(as for real gas){\displaystyle C_{p}={\frac {5}{2}}nR\;}
(for monatomic ideal gas)

{\displaystyle C_{p}={\frac {7}{2}}nR\;}
(for diatomic ideal gas)

{\displaystyle C_{V}={\frac {3}{2}}nR\;}
(for monatomic ideal gas)

{\displaystyle C_{V}={\frac {5}{2}}nR\;}
(for diatomic ideal gas)

Internal Energy
ΔU{\displaystyle \Delta U=C_{V}\Delta T\;}{\displaystyle Q+W\;}

{\displaystyle Q_{p}-p\Delta V\;}{\displaystyle Q\;}

{\displaystyle C_{V}\left(T_{2}-T_{1}\right)\;}{\displaystyle 0\;}

{\displaystyle Q=-W\;}{\displaystyle W\;}

{\displaystyle C_{V}\left(T_{2}-T_{1}\right)\;}Enthalpy
ΔH{\displaystyle H=U+pV\;}{\displaystyle C_{p}\left(T_{2}-T_{1}\right)\;}{\displaystyle Q_{V}+V\Delta p\;}{\displaystyle 0\;}{\displaystyle C_{p}\left(T_{2}-T_{1}\right)\;}Entropy
Δs{\displaystyle \Delta S=C_{V}\ln {T_{2} \over T_{1}}+nR\ln {V_{2} \over V_{1}}}
{\displaystyle \Delta S=C_{p}\ln {T_{2} \over T_{1}}-nR\ln {p_{2} \over p_{1}}}[1]{\displaystyle C_{p}\ln {\frac {T_{2}}{T_{1}}}\;}{\displaystyle C_{V}\ln {\frac {T_{2}}{T_{1}}}\;}{\displaystyle nR\ln {\frac {V_{2}}{V_{1}}}\;}
{\displaystyle {\frac {Q}{T}}\;}{\displaystyle C_{p}\ln {\frac {V_{2}}{V_{1}}}+C_{V}\ln {\frac {p_{2}}{p_{1}}}=0\;}Constant{\displaystyle \;}{\displaystyle {\frac {V}{T}}\;}{\displaystyle {\frac {p}{T}}\;}{\displaystyle pV\;}{\displaystyle pV^{\gamma }\;}