Thermodynamical functions

ChemistryLab.thermo_function_library
ChemistryLab.Callable
ChemistryLab.ThermoFunction
ChemistryLab.ThermoFunction
ChemistryLab.apply
ChemistryLab.calculate_molar_mass
ChemistryLab.∂
ChemistryLab.∫

ChemistryLab.Callable — Type

Callable

Abstract base type for all callable thermodynamic functions.

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ChemistryLab.ThermoFunction — Type

ThermoFunction{U,F,R} <: Callable

Representation of a thermodynamic function with symbolic expression, variables, units, and reference conditions.

Fields

symexpr::Num: Symbolic expression of the thermodynamic function
vars::OrderedDict{Symbol,Num}: Dictionary of variables (symbols to symbolic expressions)
unit::U: Unit of the function's output
func::F: Compiled function for evaluation
ref::R: Reference conditions dictionary

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ChemistryLab.ThermoFunction — Type

ThermoFunction(expr::Union{Symbol,Expr}, params=Pair[], vars=[:T, :P, :t]; ref=[])

Construct a ThermoFunction from an expression, parameters, variables, and reference conditions.

Arguments

expr: Symbol or expression (or key from thermofunctionlibrary)
params: Parameter values as Pairs
vars: Variable symbols (default: [:T, :P, :t, :x, :y, :z])
ref: Reference conditions dictionary (default: ref=[:T => 298.15u"K", :P => 1u"bar", :t => 0u"s"])

Warning

It is possible to use or not units when defining parameters and reference values but in case of dimensioned quantities, the user should take care of the homogeneity of the expression consistently with parameters and variables units. However variables inside functions such as log, exp, cos... are assumed to be dimensionless (or better implicitly divided by a unit value in the International System of Units) so that it is possible to write log(T), exp(T), cos(T) while keeping T in Kelvins.

Examples

julia> expr = :(α + β * T + γ * log(T))
:(α + β * T + γ * log(T))

julia> params = [:α => 210.0u"J/K/mol", :β => 0.0u"J/mol/K^2", :γ => -3.07e6u"J/K/mol"]
3-element Vector{Pair{Symbol, Quantity{Float64, Dimensions{FRInt32}}}}:
 :α => 210.0 m² kg s⁻² K⁻¹ mol⁻¹
 :β => 0.0 m² kg s⁻² K⁻² mol⁻¹
 :γ => -3.07e6 m² kg s⁻² K⁻¹ mol⁻¹

julia> vars = [:T]
1-element Vector{Symbol}:
 :T

julia> tf = ThermoFunction(expr, params, vars; ref=[:T => 298.15u"K"])
210.0 - 3.07e6log(T) ♢ unit=[m² kg s⁻² K⁻¹ mol⁻¹] ♢ ref=[T=298.15 K]

julia> tf() # default evaluation at reference variable here Tref=298.15K
-1.7491411916797183e7 m² kg s⁻² K⁻¹ mol⁻¹

julia> tf(300.0u"K")
-1.7510402197194535e7 m² kg s⁻² K⁻¹ mol⁻¹

julia> tf(300.0)
-1.7510402197194535e7

julia> tf_nounits = ThermoFunction(expr, [:α => 210.0, :β => 0.0, :γ => -3.07e6], vars; ref=[:T => 298.15])
210.0 - 3.07e6log(T) ♢ unit=[] ♢ ref=[T=298.15]

julia> tf_nounits(300.0u"K")
-1.7510402197194535e7

julia> tf_nounits(300.)
-1.7510402197194535e7

Note

Note that ThermoFunction can be used as a functor i.e. can apply on a dimensioned or dimensionless value, which respectively returns a dimensioned or dimensionless result. The default argument(s) is (are) the reference one(s).

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ChemistryLab.thermo_function_library — Constant

thermo_function_library

Dictionary of predefined thermodynamic function expressions.

Contents

:Cp: Heat capacity expression
:CpoverT: Heat capacity divided by temperature
:logKr: Logarithm of equilibrium constant

Examples

julia> thermo_function_library[:Cp]
:(a₀ + a₁ * T + a₂ / T ^ 2 + a₃ / √T + a₄ * T ^ 2 + a₅ * T ^ 3 + a₆ * T ^ 4 + a₇ / T ^ 3 + a₈ / T + a₉ * √T + a₁₀ * log(T))

julia> thermo_function_library[:CpoverT]
:(a₀ / T + a₁ + a₂ / T ^ 3 + a₃ / T ^ (3 / 2) + a₄ * T + a₅ * T ^ 2 + a₆ * T ^ 3 + a₇ / T ^ 4 + a₈ / T ^ 2 + a₉ / √T + (a₁₀ * log(T)) / T)

julia> thermo_function_library[:logKr]
:(A₀ + A₁ * T + A₂ / T + A₃ * log(T) + A₄ / T ^ 2 + A₅ * T ^ 2 + A₆ * √T)

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ChemistryLab.∂ — Function

∂(tf::ThermoFunction, var=collect(keys(tf.vars))[1])

Compute the partial derivative of a thermodynamic function.

Arguments

var: Variable to differentiate with respect to (default: first variable)

Returns

New ThermoFunction representing the derivative

Examples

julia> Cp = ThermoFunction(:Cp, [:a₀ => 210.0u"J/K/mol", :a₁ => 0.12u"J/mol/K^2", :a₂ => -3.07e6u"J*K/mol", :a₃ => 0.0u"J/mol/√K"]; ref=[:T => 298.15u"K", :P => 1u"bar"])
210.0 + 0.12T + -3.07e6 / (T^2) ♢ unit=[m² kg s⁻² K⁻¹ mol⁻¹] ♢ ref=[T=298.15 K, P=100000.0 m⁻¹ kg s⁻²]

julia> ∂(Cp)
0.12 + 6.14e6 / (T^3) ♢ unit=[m² kg s⁻² K⁻² mol⁻¹] ♢ ref=[T=298.15 K, P=100000.0 m⁻¹ kg s⁻²]

julia> rate = ThermoFunction(:((c₁+c₂*t)/(c₃+c₄*√t)), [:c₁ => 1.0, :c₂ => 2.0u"1/s", :c₃ => 3.0, :c₄ => 4.0u"1/√s"])
(1.0 + 2.0t) / (3.0 + 4.0sqrt(t)) ♢ unit=[] ♢ ref=[t=0.0 s]

julia> ∂(rate)(1u"h")
0.004165467097946903 s⁻¹

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ChemistryLab.∫ — Function

∫(tf::ThermoFunction, var=collect(keys(tf.vars))[1])

Compute the integral of a thermodynamic function.

Arguments

var: Variable to integrate with respect to (default: first variable)

Returns

New ThermoFunction representing the integral

Examples

julia> Cp = ThermoFunction(:Cp, [:a₀ => 210.0u"J/K/mol", :a₁ => 0.12u"J/mol/K^2", :a₂ => -3.07e6u"J*K/mol", :a₃ => 0.0u"J/mol/√K"]; ref=[:T => 298.15u"K", :P => 1u"bar"])
210.0 + 0.12T + -3.07e6 / (T^2) ♢ unit=[m² kg s⁻² K⁻¹ mol⁻¹] ♢ ref=[T=298.15 K, P=100000.0 m⁻¹ kg s⁻²]

julia> ∫Cp = ∫(Cp)
210.0T + 3.07e6 / T + 0.06(T^2) ♢ unit=[m² kg s⁻² mol⁻¹] ♢ ref=[T=298.15 K, P=100000.0 m⁻¹ kg s⁻²]

julia> ΔfH⁰_Tref = -2.72e6u"J/mol"
-2.72e6 m² kg s⁻² mol⁻¹

julia> ΔfH⁰ = (ΔfH⁰_Tref -∫Cp()) + ∫Cp
-2.798241935804469e6 + 210.0T + 3.07e6 / T + 0.06(T^2) ♢ unit=[m² kg s⁻² mol⁻¹] ♢ ref=[T=298.15 K, P=100000.0 m⁻¹ kg s⁻²]

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ChemistryLab.calculate_molar_mass — Function

calculate_molar_mass(atoms::AbstractDict{Symbol,T}) where {T<:Number} -> Quantity

Calculate the molar mass from an atomic composition dictionary.

Arguments

atoms: dictionary mapping element symbols to stoichiometric coefficients.

Returns

Molar mass as a Quantity in g/mol units.

Examples

julia> calculate_molar_mass(OrderedDict(:H => 2, :O => 1))
0.0180149999937744 kg mol⁻¹

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ChemistryLab.apply — Function

apply(func::Function, tf::ThermoFunction, args...; kwargs...)

Apply a function to a thermodynamic function's expression.

Arguments

func: Function to apply
tf: ThermoFunction
args...: Additional arguments for func
kwargs...: Additional keyword arguments

Returns

New ThermoFunction with transformed expression

Examples

julia> f = ThermoFunction(:(a+b*x), [:a=>3, :b=>2])
3 + 2x ♢ unit=[] ♢ ref=[x=0]

julia> apply(expand∘(x->x^2), f)
9 + 12x + 4(x^2) ♢ unit=[] ♢ ref=[x=0]

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apply(func::Function, f::Formula, args...; kwargs...) -> Formula

Element-wise apply func to all numeric components of f and to its charge. Quantities are handled, attempting to preserve dimensions when possible.

Examples

julia> result = apply(x -> x*2, Formula("H2O"));

julia> result[:H]
4

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apply(func::Function, s::S, args...; kwargs...) where {S<:AbstractSpecies} -> S

Apply a function element-wise to all numeric components and properties of a species.

Arguments

func: function to apply.
s: source species.
args...: additional arguments for func.
kwargs...: keyword arguments (including potential overrides for name, symbol, etc.).

Returns

New species with transformed values.

Handles Quantity types, attempting to preserve dimensions when possible.

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apply(func::Function, r::Reaction{SR,TR,SP,TP}, args...; kwargs...) where {SR<:AbstractSpecies,TR<:Number,SP<:AbstractSpecies,TP<:Number}

Apply a function to all species and coefficients in a reaction.

Arguments

func: function to apply to species and coefficients
r: reaction to transform
args...: additional arguments for func
kwargs...: additional keyword arguments

Returns

A new Reaction with transformed species and coefficients

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