थर्मोडायनामिक समीकरणों की तालिका

For इन समीकरणों में प्रयुक्त गणित अंकन की सूची, see गणितीय अंकन.

Main article: थर्मोडायनामिक गुणों की सूची

यह लेख ऊष्मप्रवैगिकी में सामान्य समीकरण और भौतिक मात्रा का सारांश है (अधिक विस्तार के लिए ऊष्मप्रवैगिकी समीकरण देखें)।

परिभाषाएँ

Main articles: ऊष्मागतिक गुणों की सूची, ऊष्मागतिक विभव, मुक्त एन्ट्रापी, and परिभाषित समीकरण (भौतिक रसायन विज्ञान)

नीचे दी गई कई परिभाषाएँ रासायनिक प्रतिक्रियाओं के ऊष्मप्रवैगिकी में भी उपयोग की जाती हैं।

सामान्य मूल मात्रा

मात्रा (सामान्य नाम)	(सामान्य) प्रतीक	एसआई इकाइयां	आयाम
अणुओं की संख्या	N	विमाहीन	विमाहीन
मोल्स की संख्या	n	mol	[N]
तापमान	T	K	[Θ]
ऊष्मा ऊर्जा	Q, q	J	[M][L]2[T]−2
गुप्त ऊष्मा	QL	J	[M][L]2[T]−2

सामान्य व्युत्पन्न मात्रा

Quantity (Common Name/s)	(Common) Symbol/s	Defining Equation	SI Units	Dimension
Thermodynamic beta, Inverse temperature	β	$\beta =1/k_{B}T\,\!$	J−1	[T]2[M]−1[L]−2
Thermodynamic temperature	τ	$\tau =k_{B}T\,\!$ $\tau =k_{B}\left(\partial U/\partial S\right)_{N}\,\!$ $1/\tau =1/k_{B}\left(\partial S/\partial U\right)_{N}\,\!$	J	[M] [L]2 [T]−2
Entropy	S	$S=-k_{B}\sum _{i}p_{i}\ln p_{i}$ $S=-\left(\partial F/\partial T\right)_{V}\,\!$ , $S=-\left(\partial G/\partial T\right)_{N,P}\,\!$	J K−1	[M][L]2[T]−2 [Θ]−1
Pressure	P	$P=-\left(\partial F/\partial V\right)_{T,N}\,\!$ $P=-\left(\partial U/\partial V\right)_{S,N}\,\!$	Pa	M L−1T−2
Internal Energy	U	$U=\sum _{i}E_{i}\!$	J	[M][L]2[T]−2
Enthalpy	H	$H=U+pV\,\!$	J	[M][L]2[T]−2
Partition Function	Z		dimensionless	dimensionless
Gibbs free energy	G	$G=H-TS\,\!$	J	[M][L]2[T]−2
Chemical potential (of component i in a mixture)	μi	$\mu _{i}=\left(\partial U/\partial N_{i}\right)_{N_{j\neq i},S,V}\,\!$ $\mu _{i}=\left(\partial F/\partial N_{i}\right)_{T,V}\,\!$, where F is not proportional to N because μi depends on pressure. $\mu _{i}=\left(\partial G/\partial N_{i}\right)_{T,P}\,\!$, where G is proportional to N (as long as the molar ratio composition of the system remains the same) because μi depends only on temperature and pressure and composition. $\mu _{i}/\tau =-1/k_{B}\left(\partial S/\partial N_{i}\right)_{U,V}\,\!$	J	[M][L]2[T]−2
Helmholtz free energy	A, F	$F=U-TS\,\!$	J	[M][L]2[T]−2
Landau potential, Landau Free Energy, Grand potential	Ω, ΦG	$\Omega =U-TS-\mu N\,\!$	J	[M][L]2[T]−2
Massieu Potential, Helmholtz free entropy	Φ	$\Phi =S-U/T\,\!$	J K−1	[M][L]2[T]−2 [Θ]−1
Planck potential, Gibbs free entropy	Ξ	$\Xi =\Phi -pV/T\,\!$	J K−1	[M][L]2[T]−2 [Θ]−1

पदार्थ के ऊष्मीय गुण

Main articles: ऊष्मा धारिता and तापीय प्रसार

Quantity (common name/s)	(Common) symbol/s	Defining equation	SI units	Dimension
General heat/thermal capacity	C	$C=\partial Q/\partial T\,\!$	J K −1	[M][L]2[T]−2 [Θ]−1
Heat capacity (isobaric)	Cp	$C_{p}=\partial H/\partial T\,\!$	J K −1	[M][L]2[T]−2 [Θ]−1
Specific heat capacity (isobaric)	Cmp	$C_{mp}=\partial ^{2}Q/\partial m\partial T\,\!$	J kg−1 K−1	[L]2[T]−2 [Θ]−1
Molar specific heat capacity (isobaric)	Cnp	$C_{np}=\partial ^{2}Q/\partial n\partial T\,\!$	J K −1 mol−1	[M][L]2[T]−2 [Θ]−1 [N]−1
Heat capacity (isochoric/volumetric)	CV	$C_{V}=\partial U/\partial T\,\!$	J K −1	[M][L]2[T]−2 [Θ]−1
Specific heat capacity (isochoric)	CmV	$C_{mV}=\partial ^{2}Q/\partial m\partial T\,\!$	J kg−1 K−1	[L]2[T]−2 [Θ]−1
Molar specific heat capacity (isochoric)	CnV	$C_{nV}=\partial ^{2}Q/\partial n\partial T\,\!$	J K −1 mol−1	[M][L]2[T]−2 [Θ]−1 [N]−1
Specific latent heat	L	$L=\partial Q/\partial m\,\!$	J kg−1	[L]2[T]−2
Ratio of isobaric to isochoric heat capacity, heat capacity ratio, adiabatic index	γ	$\gamma =C_{p}/C_{V}=c_{p}/c_{V}=C_{mp}/C_{mV}\,\!$	dimensionless	dimensionless

थर्मल ट्रांसफर

Main article: ऊष्मीय चालकता

Quantity (common name/s)	(Common) symbol/s	Defining equation	SI units	Dimension
Temperature gradient	No standard symbol	$\nabla T\,\!$	K m−1	[Θ][L]−1
Thermal conduction rate, thermal current, thermal/heat flux, thermal power transfer	P	$P=\mathrm {d} Q/\mathrm {d} t\,\!$	W = J s−1	[M] [L]2 [T]−3
Thermal intensity	I	$I=\mathrm {d} P/\mathrm {d} A$	W m−2	[M] [T]−3
Thermal/heat flux density (vector analogue of thermal intensity above)	q	$Q=\iint \mathbf {q} \cdot \mathrm {d} \mathbf {S} \mathrm {d} t\,\!$	W m−2	[M] [T]−3

समीकरण

इस लेख के समीकरणों को विषय द्वारा वर्गीकृत किया गया है।

ऊष्मागतिक प्रक्रियाएं

Physical situation	Equations
Isentropic process (adiabatic and reversible)	$Q=0,\quad \Delta U=-W\,\!$ For an ideal gas $p_{1}V_{1}^{\gamma }=p_{2}V_{2}^{\gamma }\,\!$ $T_{1}V_{1}^{\gamma -1}=T_{2}V_{2}^{\gamma -1}\,\!$ $p_{1}^{1-\gamma }T_{1}^{\gamma }=p_{2}^{1-\gamma }T_{2}^{\gamma }\,\!$
Isothermal process	$\Delta U=0,\quad W=Q\,\!$ For an ideal gas $W=kTN\ln(V_{2}/V_{1})\,\!$ $W=nRT\ln(V_{2}/V_{1})\,\!$
Isobaric process	p1 = p2, p = constant $W=p\Delta V,\quad Q=\Delta U+p\delta V\,\!$
Isochoric process	V1 = V2, V = constant $W=0,\quad Q=\Delta U\,\!$
Free expansion	$\Delta U=0\,\!$
Work done by an expanding gas	Process $W=\int _{V_{1}}^{V_{2}}p\mathrm {d} V\,\!$ Net Work Done in Cyclic Processes $W=\oint _{\mathrm {cycle} }p\mathrm {d} V=\oint _{\mathrm {cycle} }\Delta Q\,\!$

गतिज सिद्धांत

Ideal gas equations

Physical situation	Nomenclature	Equations
Ideal gas law	p = pressure V = volume of container T = temperature n = number of moles R = Gas constant N = number of molecules k = Boltzmann's constant	$pV=nRT=kTN\,\!$ ${\frac {p_{1}V_{1}}{p_{2}V_{2}}}={\frac {n_{1}T_{1}}{n_{2}T_{2}}}={\frac {N_{1}T_{1}}{N_{2}T_{2}}}\,\!$
Pressure of an ideal gas	m = mass of one molecule Mm = molar mass	$p={\frac {Nm\langle v^{2}\rangle }{3V}}={\frac {nM_{m}\langle v^{2}\rangle }{3V}}={\frac {1}{3}}\rho \langle v^{2}\rangle \,\!$

आदर्श गैस

Quantity	General Equation	Isobaric Δp = 0	Isochoric ΔV = 0	Isothermal ΔT = 0	Adiabatic $Q=0$
Work W	$\delta W=-pdV\;$	$-p\Delta V\;$	$0\;$	$-nRT\ln {\frac {V_{2}}{V_{1}}}\;$ $-nRT\ln {\frac {P_{1}}{P_{2}}}\;$	${\frac {PV^{\gamma }(V_{f}^{1-\gamma }-V_{i}^{1-\gamma })}{1-\gamma }}=C_{V}\left(T_{2}-T_{1}\right)$
Heat Capacity C	(as for real gas)	$C_{p}={\frac {5}{2}}nR\;$ (for monatomic ideal gas) $C_{p}={\frac {7}{2}}nR\;$ (for diatomic ideal gas)	$C_{V}={\frac {3}{2}}nR\;$ (for monatomic ideal gas) $C_{V}={\frac {5}{2}}nR\;$ (for diatomic ideal gas)
Internal Energy ΔU	$\Delta U=C_{V}\Delta T\;$	$Q+W\;$ $Q_{p}-p\Delta V\;$	$Q\;$ $C_{V}\left(T_{2}-T_{1}\right)\;$	$0\;$ $Q=-W\;$	$W\;$ $C_{V}\left(T_{2}-T_{1}\right)\;$
Enthalpy ΔH	$H=U+pV\;$	$C_{p}\left(T_{2}-T_{1}\right)\;$	$Q_{V}+V\Delta p\;$	$0\;$	$C_{p}\left(T_{2}-T_{1}\right)\;$
Entropy Δs	$\Delta S=C_{V}\ln {T_{2} \over T_{1}}+nR\ln {V_{2} \over V_{1}}$ $\Delta S=C_{p}\ln {T_{2} \over T_{1}}-nR\ln {p_{2} \over p_{1}}$	$C_{p}\ln {\frac {T_{2}}{T_{1}}}\;$	$C_{V}\ln {\frac {T_{2}}{T_{1}}}\;$	$nR\ln {\frac {V_{2}}{V_{1}}}\;$ ${\frac {Q}{T}}\;$	$C_{p}\ln {\frac {V_{2}}{V_{1}}}+C_{V}\ln {\frac {p_{2}}{p_{1}}}=0\;$
Constant	$\;$	${\frac {V}{T}}\;$	${\frac {p}{T}}\;$	$pV\;$	$pV^{\gamma }\;$

एंट्रॉपी

• $S=k_{\mathrm {B} }\ln \Omega$, जहां k_B बोल्ट्ज़मैन स्थिरांक है, और Ω चरण स्थान में स्थूल अवस्था की मात्रा को दर्शाता है या अन्यथा ऊष्मागतिक संभाव्यता कहा जाता है।
• $dS={\frac {\delta Q}{T}}$, केवल प्रतिवर्ती प्रक्रियाओं के लिए

सांख्यिकीय भौतिकी

नीचे एक आदर्श गैस के लिए मैक्सवेल-बोल्ट्ज़मैन वितरण से उपयोगी परिणाम और एंट्रॉपी मात्रा के निहितार्थ हैं। वितरण आदर्श गैस बनाने वाले परमाणुओं या अणुओं के लिए मान्य है।

Physical situation	Nomenclature	Equations
Maxwell–Boltzmann distribution	v = velocity of atom/molecule, m = mass of each molecule (all molecules are identical in kinetic theory), γ(p) = Lorentz factor as function of momentum (see below) Ratio of thermal to rest mass-energy of each molecule:$\theta =k_{B}T/mc^{2}\,\!$ K2 is the Modified Bessel function of the second kind.	Non-relativistic speeds $P\left(v\right)=4\pi \left({\frac {m}{2\pi k_{B}T}}\right)^{3/2}v^{2}e^{-mv^{2}/2k_{B}T}\,\!$ Relativistic speeds (Maxwell-Jüttner distribution) $f(p)={\frac {1}{4\pi m^{3}c^{3}\theta K_{2}(1/\theta )}}e^{-\gamma (p)/\theta }$
Entropy Logarithm of the density of states	Pi = probability of system in microstate i Ω = total number of microstates	$S=-k_{B}\sum _{i}P_{i}\ln P_{i}=k_{\mathrm {B} }\ln \Omega \,\!$ where: $P_{i}=1/\Omega \,\!$
Entropy change		$\Delta S=\int _{Q_{1}}^{Q_{2}}{\frac {\mathrm {d} Q}{T}}\,\!$ $\Delta S=k_{B}N\ln {\frac {V_{2}}{V_{1}}}+NC_{V}\ln {\frac {T_{2}}{T_{1}}}\,\!$
Entropic force		$\mathbf {F} _{\mathrm {S} }=-T\nabla S\,\!$
Equipartition theorem	df = degree of freedom	Average kinetic energy per degree of freedom $\langle E_{\mathrm {k} }\rangle ={\frac {1}{2}}kT\,\!$ Internal energy $U=d_{f}\langle E_{\mathrm {k} }\rangle ={\frac {d_{f}}{2}}kT\,\!$

गैर-सापेक्षवादी मैक्सवेल-बोल्ट्जमान वितरण के परिणाम नीचे दिए गए हैं।

Physical situation	Nomenclature	Equations
Mean speed		$\langle v\rangle ={\sqrt {\frac {8k_{B}T}{\pi m}}}\,\!$
Root mean square speed		$v_{\mathrm {rms} }={\sqrt {\langle v^{2}\rangle }}={\sqrt {\frac {3k_{B}T}{m}}}\,\!$
Modal speed		$v_{\mathrm {mode} }={\sqrt {\frac {2k_{B}T}{m}}}\,\!$
Mean free path	σ = Effective cross-section n = Volume density of number of target particles ℓ = Mean free path	$\ell =1/{\sqrt {2}}n\sigma \,\!$

अर्ध-स्थैतिक और प्रतिवर्ती प्रक्रियाएं

अर्ध-स्थैतिक प्रक्रिया | अर्ध-स्थैतिक और प्रतिवर्ती प्रक्रिया (ऊष्मागतिक्स) प्रक्रियाओं के लिए, ऊष्मप्रवैगिकी का पहला नियम है:

$dU=\delta Q-\delta W$

जहाँ δQ तंत्र को आपूर्ति की गई ऊष्मा है और δW निकाय द्वारा किया गया कार्य है।

ऊष्मागतिक क्षमता

Main article: ऊष्मागतिक विभव

See also: Maxwell relations

निम्नलिखित ऊर्जाओं को ऊष्मागतिक क्षमता कहा जाता है,

Name	Symbol	Formula	Natural variables
Internal energy	$U$	$\int \left(T\,\mathrm {d} S-p\,\mathrm {d} V+\sum _{i}\mu _{i}\mathrm {d} N_{i}\right)$	$S,V,\{N_{i}\}$
Helmholtz free energy	$F$	$U-TS$	$T,V,\{N_{i}\}$
Enthalpy	$H$	$U+pV$	$S,p,\{N_{i}\}$
Gibbs free energy	$G$	$U+pV-TS$	$T,p,\{N_{i}\}$
Landau potential, or grand potential	$\Omega$, $\Phi _{\text{G}}$	$U-TS-$$\sum _{i}\,$$\mu _{i}N_{i}$	$T,V,\{\mu _{i}\}$

और संबंधित मूलभूत ऊष्मागतिक संबंध या मास्टर समीकरण हैं:

Potential	Differential
Internal energy	$dU\left(S,V,{N_{i}}\right)=TdS-pdV+\sum _{i}\mu _{i}dN_{i}$
Enthalpy	$dH\left(S,p,{N_{i}}\right)=TdS+Vdp+\sum _{i}\mu _{i}dN_{i}$
Helmholtz free energy	$dF\left(T,V,{N_{i}}\right)=-SdT-pdV+\sum _{i}\mu _{i}dN_{i}$
Gibbs free energy	$dG\left(T,p,{N_{i}}\right)=-SdT+Vdp+\sum _{i}\mu _{i}dN_{i}$

मैक्सवेल के संबंध

मैक्सवेल के चार सबसे आम संबंध हैं:

Physical situation	Nomenclature	Equations
Thermodynamic potentials as functions of their natural variables	$U(S,V)\,$ = Internal energy $H(S,P)\,$ = Enthalpy $F(T,V)\,$ = Helmholtz free energy $G(T,P)\,$ = Gibbs free energy	$\left({\frac {\partial T}{\partial V}}\right)_{S}=-\left({\frac {\partial P}{\partial S}}\right)_{V}={\frac {\partial ^{2}U}{\partial S\partial V}}$ $\left({\frac {\partial T}{\partial P}}\right)_{S}=+\left({\frac {\partial V}{\partial S}}\right)_{P}={\frac {\partial ^{2}H}{\partial S\partial P}}$ $+\left({\frac {\partial S}{\partial V}}\right)_{T}=\left({\frac {\partial P}{\partial T}}\right)_{V}=-{\frac {\partial ^{2}F}{\partial T\partial V}}$ $-\left({\frac {\partial S}{\partial P}}\right)_{T}=\left({\frac {\partial V}{\partial T}}\right)_{P}={\frac {\partial ^{2}G}{\partial T\partial P}}$

अधिक संबंधों में निम्नलिखित शामिल हैं।

$\left({\partial S \over \partial U}\right)_{V,N}={1 \over T}$	$\left({\partial S \over \partial V}\right)_{N,U}={p \over T}$	$\left({\partial S \over \partial N}\right)_{V,U}=-{\mu \over T}$
$\left({\partial T \over \partial S}\right)_{V}={T \over C_{V}}$	$\left({\partial T \over \partial S}\right)_{P}={T \over C_{P}}$
$-\left({\partial p \over \partial V}\right)_{T}={1 \over {VK_{T}}}$

अन्य अंतर समीकरण हैं:

Name	H	U	G
Gibbs–Helmholtz equation	$H=-T^{2}\left({\frac {\partial \left(G/T\right)}{\partial T}}\right)_{p}$	$U=-T^{2}\left({\frac {\partial \left(F/T\right)}{\partial T}}\right)_{V}$	$G=-V^{2}\left({\frac {\partial \left(F/V\right)}{\partial V}}\right)_{T}$
	$\left({\frac {\partial H}{\partial p}}\right)_{T}=V-T\left({\frac {\partial V}{\partial T}}\right)_{P}$	$\left({\frac {\partial U}{\partial V}}\right)_{T}=T\left({\frac {\partial P}{\partial T}}\right)_{V}-P$

क्वांटम गुण

• $U=Nk_{B}T^{2}\left({\frac {\partial \ln Z}{\partial T}}\right)_{V}~$
• $S={\frac {U}{T}}+Nk_{B}\ln Z-Nk\ln N+Nk~$ अप्रभेद्य कण

जहाँ N कणों की संख्या है, h प्लैंक नियतांक है, I जड़त्वाघूर्ण है, और Z विभिन्न रूपों में विभाजन फलन (सांख्यिकीय यांत्रिकी) है:

Degree of freedom	Partition function
Translation	$Z_{t}={\frac {(2\pi mk_{B}T)^{\frac {3}{2}}V}{h^{3}}}$
Vibration	$Z_{v}={\frac {1}{1-e^{\frac {-h\omega }{2\pi k_{B}T}}}}$
Rotation	$Z_{r}={\frac {2Ik_{B}T}{\sigma ({\frac {h}{2\pi }})^{2}}}$ where: σ = 1 (heteronuclear molecules) σ = 2 (homonuclear)

पदार्थ के ऊष्मीय गुण

Coefficients	Equation
Joule-Thomson coefficient	$\mu _{JT}=\left({\frac {\partial T}{\partial p}}\right)_{H}$
Compressibility (constant temperature)	$K_{T}=-{1 \over V}\left({\partial V \over \partial p}\right)_{T,N}$
Coefficient of thermal expansion (constant pressure)	$\alpha _{p}={\frac {1}{V}}\left({\frac {\partial V}{\partial T}}\right)_{p}$
Heat capacity (constant pressure)	$C_{p}=\left({\partial Q_{rev} \over \partial T}\right)_{p}=\left({\partial U \over \partial T}\right)_{p}+p\left({\partial V \over \partial T}\right)_{p}=\left({\partial H \over \partial T}\right)_{p}=T\left({\partial S \over \partial T}\right)_{p}$
Heat capacity (constant volume)	$C_{V}=\left({\partial Q_{rev} \over \partial T}\right)_{V}=\left({\partial U \over \partial T}\right)_{V}=T\left({\partial S \over \partial T}\right)_{V}$

Derivation of heat capacity (constant pressure)

Since $\left({\frac {\partial T}{\partial p}}\right)_{H}\left({\frac {\partial p}{\partial H}}\right)_{T}\left({\frac {\partial H}{\partial T}}\right)_{p}=-1$ ${\begin{aligned}\left({\frac {\partial T}{\partial p}}\right)_{H}&=-\left({\frac {\partial H}{\partial p}}\right)_{T}\left({\frac {\partial T}{\partial H}}\right)_{p}\\&={\frac {-1}{\left({\frac {\partial H}{\partial T}}\right)_{p}}}\left({\frac {\partial H}{\partial p}}\right)_{T}\end{aligned}}$ $C_{p}=\left({\frac {\partial H}{\partial T}}\right)_{p}$ $\Rightarrow \left({\frac {\partial T}{\partial p}}\right)_{H}=-{\frac {1}{C_{p}}}\left({\frac {\partial H}{\partial p}}\right)_{T}$

Derivation of heat capacity (constant volume)

Since $dU=\delta Q_{rev}-\delta W_{rev},$ (where δWrev is the work done by the system), $\delta S={\frac {\delta Q_{rev}}{T}},\delta W_{rev}=p\delta V$ $dU=T\delta S-p\delta V$ $\left({\frac {\partial U}{\partial T}}\right)_{V}=T\left({\frac {\partial S}{\partial T}}\right)_{V}-p\left({\frac {\partial V}{\partial T}}\right)_{V};C_{V}=\left({\frac {\partial U}{\partial T}}\right)_{V}$ $\Rightarrow C_{V}=T\left({\frac {\partial S}{\partial T}}\right)_{V}$

तापीय स्थानांतरण

Physical situation	Nomenclature	Equations
Net intensity emission/absorption	Texternal = external temperature (outside of system) Tsystem = internal temperature (inside system) ε = emmisivity	$I=\sigma \epsilon \left(T_{\mathrm {external} }^{4}-T_{\mathrm {system} }^{4}\right)\,\!$
Internal energy of a substance	CV = isovolumetric heat capacity of substance ΔT = temperature change of substance	$\Delta U=NC_{V}\Delta T\,\!$
Meyer's equation	Cp = isobaric heat capacity CV = isovolumetric heat capacity n = number of moles	$C_{p}-C_{V}=nR\,\!$
Effective thermal conductivities	λi = thermal conductivity of substance i λnet = equivalent thermal conductivity	Series $\lambda _{\mathrm {net} }=\sum _{j}\lambda _{j}\,\!$ Parallel ${\frac {1}{\lambda }}_{\mathrm {net} }=\sum _{j}\left({\frac {1}{\lambda }}_{j}\right)\,\!$

तापीय क्षमता

Physical situation	Nomenclature	Equations
Thermodynamic engines	η = efficiency W = work done by engine QH = heat energy in higher temperature reservoir QL = heat energy in lower temperature reservoir TH = temperature of higher temp. reservoir TL = temperature of lower temp. reservoir	Thermodynamic engine: $\eta =\left|{\frac {W}{Q_{H}}}\right|\,\!$ Carnot engine efficiency: $\eta _{c}=1-\left|{\frac {Q_{L}}{Q_{H}}}\right|=1-{\frac {T_{L}}{T_{H}}}\,\!$
Refrigeration	K = coefficient of refrigeration performance	Refrigeration performance $K=\left|{\frac {Q_{L}}{W}}\right|\,\!$ Carnot refrigeration performance $K_{C}={\frac {|Q_{L}|}{|Q_{H}|-|Q_{L}|}}={\frac {T_{L}}{T_{H}-T_{L}}}\,\!$

यह भी देखें

• एंटोनी समीकरण
• बेजान संख्या
• बोवेन अनुपात
• ब्रिजमैन के थर्मोडायनामिक समीकरण|ब्रिजमैन के समीकरण
• क्लॉसियस-क्लैपेरॉन संबंध
• प्रस्थान समारोह
• डुहेम-मार्ग्यूल्स समीकरण
• एहरेनफेस्ट समीकरण
• गिब्स-हेल्महोल्त्ज़ समीकरण
• चरण नियम
• कोप्प का नियम
• संबंधित राज्यों का नोरो-फ्रेनकेल नियम
• ऑनसेजर पारस्परिक संबंध
• स्टीफन संख्या
• ट्रिपल उत्पाद नियम
• सटीक अंतर

संदर्भ

• Atkins, Peter and de Paula, Julio Physical Chemistry, 7th edition, W.H. Freeman and Company, 2002 ISBN 0-7167-3539-3.
  • Chapters 1–10, Part 1: "Equilibrium".
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