Isobaric potential of temperature dependent heat capacity ========================================================= The isobaric potential of a reaction is a value whose change during a chemical reaction is equal to the change in the internal energy of the system. The isobaric potential shows how much of the total internal energy of the system can be used for chemical transformations. Thermal effect of reaction is enthalpy of the system. The heat capacity coefficients are tabular values for the reaction. They are used to express the dependence of heat capacity on temperature. **Notation:** #. :math:`T_\text{lab}` (:code:`T_lab`) is :attr:`~symplyphysics.quantities.standard_laboratory_temperature`. **Conditions:** #. We take into account the dependence of heat capacity on temperature according to the Temkin-Schwarzman formula. #. The process is isobaric-isothermal. .. TODO: find link TODO: fix file and documentation name TODO: find reference to the 'Temkin-Schwarzman formula' .. py:currentmodule:: symplyphysics.laws.thermodynamics.isobaric_potential_of_temperature_dependent_heat_capacity .. py:data:: molar_gibbs_energy_change :attr:`~symplyphysics.symbols.thermodynamics.gibbs_energy` change, or isobaric potential, per unit :attr:`~symplyphysics.symbols.chemistry.amount_of_substance`. Symbol: :code:`Delta(G_m)` Latex: :math:`\Delta G_\text{m}` Dimension: :code:`energy/amount_of_substance` .. py:data:: molar_enthalpy_change :attr:`~symplyphysics.symbols.thermodynamics.enthalpy` change, or thermal effect, per unit :attr:`~symplyphysics.symbols.chemistry.amount_of_substance`. Symbol: :code:`Delta(H_m)` Latex: :math:`\Delta H_\text{m}` Dimension: :code:`energy/amount_of_substance` .. py:data:: molar_entropy :attr:`~symplyphysics.symbols.thermodynamics.entropy` per unit :attr:`~symplyphysics.symbols.chemistry.amount_of_substance`. Symbol: :code:`S_m` Latex: :math:`S_\text{m}` Dimension: :code:`energy/(amount_of_substance*temperature)` .. py:data:: temperature :attr:`~symplyphysics.symbols.thermodynamics.temperature`. Symbol: :code:`T` Latex: :math:`T` Dimension: :code:`temperature` .. py:data:: first_capacity_coefficient First tabular coefficient of heat capacity. Symbol: :code:`a` Latex: :math:`a` Dimension: :code:`energy/(amount_of_substance*temperature)` .. py:data:: second_capacity_coefficient Second tabular coefficient of heat capacity. Symbol: :code:`b` Latex: :math:`b` Dimension: :code:`energy/(amount_of_substance*temperature**2)` .. py:data:: third_capacity_coefficient Third tabular coefficient of heat capacity. Symbol: :code:`c` Latex: :math:`c` Dimension: :code:`energy*temperature/amount_of_substance` .. py:data:: law :code:`Delta(G_m) = Delta(H_m) - T * S_m - T * (a * (log(T_lab / T) + T_lab / T - 1) + b * (T / 2 + T_lab^2 / (2 * T) - T_lab) + c * (1 / (T^2 * 2) - 1 / (T_lab * T) + 1 / (T_lab^2 * 2)))` Latex: .. math:: \Delta G_\text{m} = \Delta H_\text{m} - T S_\text{m} - T \left(a \left(\log \left( \frac{T_\text{lab}}{T} \right) + \frac{T_\text{lab}}{T} - 1\right) + b \left(\frac{T}{2} + \frac{T_\text{lab}^{2}}{2 T} - T_\text{lab}\right) + c \left(\frac{1}{T^{2} \cdot 2} - \frac{1}{T_\text{lab} T} + \frac{1}{T_\text{lab}^{2} \cdot 2}\right)\right)