Dimensionless Helmholtz free energy

Basic equation
Dimensionless Helmholtz free energy

Values for calculation

Coefficient $ n $

$\text{if }\ \text{Region}= 1$

Equations in LaTeX code

\text{if }\ \text{Region}= 1

$$n=\left\{0.14632971213167, -0.84548187169114, -0.37563603672040E1, 0.33855169168385E1, -0.95791963387872, 0.15772038513228, -0.16616417199501E-1, 0.81214629983568E-3, 0.28319080123804E-3, -0.60706301565874E-3, -0.18990068218419E-1, -0.32529748770505E-1, -0.21841717175414E-1, -0.52838357969930E-4, -0.47184321073267E-3, -0.30001780793026E-3, 0.47661393906987E-4, -0.44141845330846E-5, -0.72694996297594E-15, -0.31679644845054E-4, -0.28270797985312E-5, -0.85205128120103E-9, -0.22425281908000E-5, -0.65171222895601E-6, -0.14341729937924E-12, -0.40516996860117E-6, -0.12734301741641E-8, -0.17424871230634E-9, -0.68762131295531E-18, 0.14478307828521E-19, 0.26335781662795E-22, -0.11947622640071E-22, 0.18228094581404E-23, -0.93537087292458E-25\right\}$$

$n=\left\{0.14632971213167, -0.84548187169114, -0.37563603672040E1, 0.33855169168385E1, -0.95791963387872, 0.15772038513228, -0.16616417199501E-1, 0.81214629983568E-3, 0.28319080123804E-3, -0.60706301565874E-3, -0.18990068218419E-1, -0.32529748770505E-1, -0.21841717175414E-1, -0.52838357969930E-4, -0.47184321073267E-3, -0.30001780793026E-3, 0.47661393906987E-4, -0.44141845330846E-5, -0.72694996297594E-15, -0.31679644845054E-4, -0.28270797985312E-5, -0.85205128120103E-9, -0.22425281908000E-5, -0.65171222895601E-6, -0.14341729937924E-12, -0.40516996860117E-6, -0.12734301741641E-8, -0.17424871230634E-9, -0.68762131295531E-18, 0.14478307828521E-19, 0.26335781662795E-22, -0.11947622640071E-22, 0.18228094581404E-23, -0.93537087292458E-25\right\}$

Equations in LaTeX code

n=\left\{0.14632971213167, -0.84548187169114, -0.37563603672040E1, 0.33855169168385E1, -0.95791963387872, 0.15772038513228, -0.16616417199501E-1, 0.81214629983568E-3, 0.28319080123804E-3, -0.60706301565874E-3, -0.18990068218419E-1, -0.32529748770505E-1, -0.21841717175414E-1, -0.52838357969930E-4, -0.47184321073267E-3, -0.30001780793026E-3, 0.47661393906987E-4, -0.44141845330846E-5, -0.72694996297594E-15, -0.31679644845054E-4, -0.28270797985312E-5, -0.85205128120103E-9, -0.22425281908000E-5, -0.65171222895601E-6, -0.14341729937924E-12, -0.40516996860117E-6, -0.12734301741641E-8, -0.17424871230634E-9, -0.68762131295531E-18, 0.14478307828521E-19, 0.26335781662795E-22, -0.11947622640071E-22, 0.18228094581404E-23, -0.93537087292458E-25\right\}

$\text{else if }\ \text{Region}= 2$

Equations in LaTeX code

\text{else if }\ \text{Region}= 2

$$n=\left\{-0.17731742473213E-2, -0.17834862292358E-1, -0.45996013696365E-1, -0.57581259083432E-1, -0.50325278727930E-1, -0.33032641670203E-4, -0.18948987516315E-3, -0.39392777243355E-2, -0.43797295650573E-1, -0.26674547914087E-4, 0.20481737692309E-7, 0.43870667284435E-6, -0.32277677238570E-4, -0.15033924542148E-2, -0.40668253562649E-1, -0.78847309559367E-9, 0.12790717852285E-7, 0.48225372718507E-6, 0.22922076337661E-5, -0.16714766451061E-10, -0.21171472321355E-2, -0.23895741934104E2, -0.59059564324270E-17, -0.12621808899101E-5, -0.38946842435739E-1, 0.11256211360459E-10, -0.82311340897998E1, 0.19809712802088E-7, 0.10406965210174E-18, -0.10234747095929E-12, -0.10018179379511E-8, -0.80882908646985E-10, 0.10693031879409, -0.33662250574171, 0.89185845355421E-24, 0.30629316876232E-12, -0.42002467698208E-5, -0.59056029685639E-25, 0.37826947613457E-5, -0.12768608934681E-14, 0.73087610595061E-28, 0.55414715350778E-16, -0.94369707241210E-6\right\}$$

$n=\left\{-0.17731742473213E-2, -0.17834862292358E-1, -0.45996013696365E-1, -0.57581259083432E-1, -0.50325278727930E-1, -0.33032641670203E-4, -0.18948987516315E-3, -0.39392777243355E-2, -0.43797295650573E-1, -0.26674547914087E-4, 0.20481737692309E-7, 0.43870667284435E-6, -0.32277677238570E-4, -0.15033924542148E-2, -0.40668253562649E-1, -0.78847309559367E-9, 0.12790717852285E-7, 0.48225372718507E-6, 0.22922076337661E-5, -0.16714766451061E-10, -0.21171472321355E-2, -0.23895741934104E2, -0.59059564324270E-17, -0.12621808899101E-5, -0.38946842435739E-1, 0.11256211360459E-10, -0.82311340897998E1, 0.19809712802088E-7, 0.10406965210174E-18, -0.10234747095929E-12, -0.10018179379511E-8, -0.80882908646985E-10, 0.10693031879409, -0.33662250574171, 0.89185845355421E-24, 0.30629316876232E-12, -0.42002467698208E-5, -0.59056029685639E-25, 0.37826947613457E-5, -0.12768608934681E-14, 0.73087610595061E-28, 0.55414715350778E-16, -0.94369707241210E-6\right\}$

Equations in LaTeX code

n=\left\{-0.17731742473213E-2, -0.17834862292358E-1, -0.45996013696365E-1, -0.57581259083432E-1, -0.50325278727930E-1, -0.33032641670203E-4, -0.18948987516315E-3, -0.39392777243355E-2, -0.43797295650573E-1, -0.26674547914087E-4, 0.20481737692309E-7, 0.43870667284435E-6, -0.32277677238570E-4, -0.15033924542148E-2, -0.40668253562649E-1, -0.78847309559367E-9, 0.12790717852285E-7, 0.48225372718507E-6, 0.22922076337661E-5, -0.16714766451061E-10, -0.21171472321355E-2, -0.23895741934104E2, -0.59059564324270E-17, -0.12621808899101E-5, -0.38946842435739E-1, 0.11256211360459E-10, -0.82311340897998E1, 0.19809712802088E-7, 0.10406965210174E-18, -0.10234747095929E-12, -0.10018179379511E-8, -0.80882908646985E-10, 0.10693031879409, -0.33662250574171, 0.89185845355421E-24, 0.30629316876232E-12, -0.42002467698208E-5, -0.59056029685639E-25, 0.37826947613457E-5, -0.12768608934681E-14, 0.73087610595061E-28, 0.55414715350778E-16, -0.94369707241210E-6\right\}

$\text{else if }\ \text{Region}= 3$

Equations in LaTeX code

\text{else if }\ \text{Region}= 3

$$n=\left\{0.10658070028513E1, -0.15732845290239E2, 0.20944396974307E2, -0.76867707878716E1, 0.26185947787954E1, -0.28080781148620E1, 0.12053369696517E1, -0.84566812812502E-2, -0.12654315477714E1, -0.11524407806681E1, 0.88521043984318, -0.64207765181607, 0.38493460186671, -0.85214708824206, 0.48972281541877E1, -0.30502617256965E1, 0.39420536879154E-1, 0.12558408424308, -0.27999329698710, 0.13899799569460E1, -0.20189915023570E1, -0.82147637173963E-2, -0.47596035734923, 0.43984074473500E-1, -0.44476435428739, 0.90572070719733, 0.70522450087967, 0.10770512626332, -0.32913623258954, -0.50871062041158, -0.22175400873096E-1, 0.94260751665092E-1, 0.16436278447961, -0.13503372241348E-1, -0.14834345352472E-1, 0.57922953628084E-3, 0.32308904703711E-2, 0.80964802996215E-4, -0.16557679795037E-3, -0.44923899061815E-4\right\}$$

$n=\left\{0.10658070028513E1, -0.15732845290239E2, 0.20944396974307E2, -0.76867707878716E1, 0.26185947787954E1, -0.28080781148620E1, 0.12053369696517E1, -0.84566812812502E-2, -0.12654315477714E1, -0.11524407806681E1, 0.88521043984318, -0.64207765181607, 0.38493460186671, -0.85214708824206, 0.48972281541877E1, -0.30502617256965E1, 0.39420536879154E-1, 0.12558408424308, -0.27999329698710, 0.13899799569460E1, -0.20189915023570E1, -0.82147637173963E-2, -0.47596035734923, 0.43984074473500E-1, -0.44476435428739, 0.90572070719733, 0.70522450087967, 0.10770512626332, -0.32913623258954, -0.50871062041158, -0.22175400873096E-1, 0.94260751665092E-1, 0.16436278447961, -0.13503372241348E-1, -0.14834345352472E-1, 0.57922953628084E-3, 0.32308904703711E-2, 0.80964802996215E-4, -0.16557679795037E-3, -0.44923899061815E-4\right\}$

Equations in LaTeX code

n=\left\{0.10658070028513E1, -0.15732845290239E2, 0.20944396974307E2, -0.76867707878716E1, 0.26185947787954E1, -0.28080781148620E1, 0.12053369696517E1, -0.84566812812502E-2, -0.12654315477714E1, -0.11524407806681E1, 0.88521043984318, -0.64207765181607, 0.38493460186671, -0.85214708824206, 0.48972281541877E1, -0.30502617256965E1, 0.39420536879154E-1, 0.12558408424308, -0.27999329698710, 0.13899799569460E1, -0.20189915023570E1, -0.82147637173963E-2, -0.47596035734923, 0.43984074473500E-1, -0.44476435428739, 0.90572070719733, 0.70522450087967, 0.10770512626332, -0.32913623258954, -0.50871062041158, -0.22175400873096E-1, 0.94260751665092E-1, 0.16436278447961, -0.13503372241348E-1, -0.14834345352472E-1, 0.57922953628084E-3, 0.32308904703711E-2, 0.80964802996215E-4, -0.16557679795037E-3, -0.44923899061815E-4\right\}

$\text{else if }\ \text{Region}= 4$

Equations in LaTeX code

\text{else if }\ \text{Region}= 4

$$n=\left\{0.11670521452767E4, -0.72421316703206E6, -0.17073846940092E2, 0.12020824702470E5, -0.32325550322333E7, 0.14915108613530E2, -0.48232657361591E4, 0.40511340542057E6, -0.23855557567849, 0.65017534844798E3\right\}$$

$n=\left\{0.11670521452767E4, -0.72421316703206E6, -0.17073846940092E2, 0.12020824702470E5, -0.32325550322333E7, 0.14915108613530E2, -0.48232657361591E4, 0.40511340542057E6, -0.23855557567849, 0.65017534844798E3\right\}$

Equations in LaTeX code

n=\left\{0.11670521452767E4, -0.72421316703206E6, -0.17073846940092E2, 0.12020824702470E5, -0.32325550322333E7, 0.14915108613530E2, -0.48232657361591E4, 0.40511340542057E6, -0.23855557567849, 0.65017534844798E3\right\}

$\text{else if }\ \text{Region}= 5$

Equations in LaTeX code

\text{else if }\ \text{Region}= 5

$$n=\left\{0.15736404855259E-2, 0.90153761673944E-3, -0.50270077677648E-2, 0.22440037409485E-5, -0.41163275453471E-5, 0.37919454822955E-7\right\}$$

$n=\left\{0.15736404855259E-2, 0.90153761673944E-3, -0.50270077677648E-2, 0.22440037409485E-5, -0.41163275453471E-5, 0.37919454822955E-7\right\}$

Equations in LaTeX code

n=\left\{0.15736404855259E-2, 0.90153761673944E-3, -0.50270077677648E-2, 0.22440037409485E-5, -0.41163275453471E-5, 0.37919454822955E-7\right\}

$\text{else}$

Equations in LaTeX code

\text{else}

$$n=\left\{\right\}$$

$n=\left\{\right\}$

Equations in LaTeX code

n=\left\{\right\}

$n$

Reduced density

$δ$

Exponent $ I $

$\text{if }\ \text{Region}= 1$

Equations in LaTeX code

\text{if }\ \text{Region}= 1

$$I=\left\{0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 8, 8, 21, 23, 29, 30, 31, 32\right\}$$

$I=\left\{0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 8, 8, 21, 23, 29, 30, 31, 32\right\}$

Equations in LaTeX code

I=\left\{0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 8, 8, 21, 23, 29, 30, 31, 32\right\}

$\text{else if }\ \text{Region}= 2$

Equations in LaTeX code

\text{else if }\ \text{Region}= 2

$$I=\left\{1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 5, 6, 6, 6, 7, 7, 7, 8, 8, 9, 10, 10, 10, 16, 16, 18, 20, 20, 20, 21, 22, 23, 24, 24, 24\right\}$$

$I=\left\{1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 5, 6, 6, 6, 7, 7, 7, 8, 8, 9, 10, 10, 10, 16, 16, 18, 20, 20, 20, 21, 22, 23, 24, 24, 24\right\}$

Equations in LaTeX code

I=\left\{1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 5, 6, 6, 6, 7, 7, 7, 8, 8, 9, 10, 10, 10, 16, 16, 18, 20, 20, 20, 21, 22, 23, 24, 24, 24\right\}

$\text{else if }\ \text{Region}= 3$

Equations in LaTeX code

\text{else if }\ \text{Region}= 3

$$I=\left\{0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 8, 9, 9, 10, 10, 11\right\}$$

$I=\left\{0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 8, 9, 9, 10, 10, 11\right\}$

Equations in LaTeX code

I=\left\{0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 8, 9, 9, 10, 10, 11\right\}

$\text{else if }\ \text{Region}= 5$

Equations in LaTeX code

\text{else if }\ \text{Region}= 5

$$I=\left\{1, 1, 1, 2, 2, 3\right\}$$

$I=\left\{1, 1, 1, 2, 2, 3\right\}$

Equations in LaTeX code

I=\left\{1, 1, 1, 2, 2, 3\right\}

$\text{else}$

Equations in LaTeX code

\text{else}

$$I=\left\{\right\}$$

$I=\left\{\right\}$

Equations in LaTeX code

I=\left\{\right\}

$I$

Inverse reduced temperature

$τ$

Exponent $ J $

$\text{if }\ \text{Region}= 1$

Equations in LaTeX code

\text{if }\ \text{Region}= 1

$$J=\left\{-2, -1, 0, 1, 2, 3, 4, 5, -9, -7, -1, 0, 1, 3, -3, 0, 1, 3, 17, -4, 0, 6, -5, -2, 10, -8, -11, -6, -29, -31, -38, -39, -40, -41\right\}$$

$J=\left\{-2, -1, 0, 1, 2, 3, 4, 5, -9, -7, -1, 0, 1, 3, -3, 0, 1, 3, 17, -4, 0, 6, -5, -2, 10, -8, -11, -6, -29, -31, -38, -39, -40, -41\right\}$

Equations in LaTeX code

J=\left\{-2, -1, 0, 1, 2, 3, 4, 5, -9, -7, -1, 0, 1, 3, -3, 0, 1, 3, 17, -4, 0, 6, -5, -2, 10, -8, -11, -6, -29, -31, -38, -39, -40, -41\right\}

$\text{else if }\ \text{Region}= 2$

Equations in LaTeX code

\text{else if }\ \text{Region}= 2

$$J=\left\{0, 1, 2, 3, 6, 1, 2, 4, 7, 36, 0, 1, 3, 6, 35, 1, 2, 3, 7, 3, 16, 35, 0, 11, 25, 8, 36, 13, 4, 10, 14, 29, 50, 57, 20, 35, 48, 21, 53, 39, 26, 40, 58\right\}$$

$J=\left\{0, 1, 2, 3, 6, 1, 2, 4, 7, 36, 0, 1, 3, 6, 35, 1, 2, 3, 7, 3, 16, 35, 0, 11, 25, 8, 36, 13, 4, 10, 14, 29, 50, 57, 20, 35, 48, 21, 53, 39, 26, 40, 58\right\}$

Equations in LaTeX code

J=\left\{0, 1, 2, 3, 6, 1, 2, 4, 7, 36, 0, 1, 3, 6, 35, 1, 2, 3, 7, 3, 16, 35, 0, 11, 25, 8, 36, 13, 4, 10, 14, 29, 50, 57, 20, 35, 48, 21, 53, 39, 26, 40, 58\right\}

$\text{else if }\ \text{Region}= 3$

Equations in LaTeX code

\text{else if }\ \text{Region}= 3

$$J=\left\{0, 0, 1, 2, 7, 10, 12, 23, 2, 6, 15, 17, 0, 2, 6, 7, 22, 26, 0, 2, 4, 16, 26, 0, 2, 4, 26, 1, 3, 26, 0, 2, 26, 2, 26, 2, 26, 0, 1, 26\right\}$$

$J=\left\{0, 0, 1, 2, 7, 10, 12, 23, 2, 6, 15, 17, 0, 2, 6, 7, 22, 26, 0, 2, 4, 16, 26, 0, 2, 4, 26, 1, 3, 26, 0, 2, 26, 2, 26, 2, 26, 0, 1, 26\right\}$

Equations in LaTeX code

J=\left\{0, 0, 1, 2, 7, 10, 12, 23, 2, 6, 15, 17, 0, 2, 6, 7, 22, 26, 0, 2, 4, 16, 26, 0, 2, 4, 26, 1, 3, 26, 0, 2, 26, 2, 26, 2, 26, 0, 1, 26\right\}

$\text{else if }\ \text{Region}= 5$

Equations in LaTeX code

\text{else if }\ \text{Region}= 5

$$J=\left\{1, 2, 3, 3, 9, 7\right\}$$

$J=\left\{1, 2, 3, 3, 9, 7\right\}$

Equations in LaTeX code

J=\left\{1, 2, 3, 3, 9, 7\right\}

$\text{else}$

Equations in LaTeX code

\text{else}

$$J=\left\{\right\}$$

$J=\left\{\right\}$

Equations in LaTeX code

J=\left\{\right\}

$J$

Region

$\text{Region}$

Calculation