Molar specific heat capacities

The use of the differential is important in the physical sciences because fundamental theorems are sometimes expressed in differential form. In chemistry, for example, the laws of thermodynamics are nearly always expressed in terms of differentials. For example, it is common to work with the following formula as a means of expressing how the molar specific heat capacity at constant pressure, Cp, of a substance varies with temperature, T ... 

The specific molar specific heat capacity of the reference state, Cp, is defined differently for gas-phase and liquid-phase reactions. For gas-phase reactions, it is defined by Eq. 5.2.58,... 

Quantities or properties may either be extensive— properties that are additive for subsystems, for example mass and distance—or intensive, in which case the value is independent of the system, like temperature and pressure. Prefixes are added to some properties to further qualify their meaning, for example specific and molar. Specific heat capacity is the heat, or energy, required to raise the temperature of a given mass by an increment. The SI units for specific heat... 

This relation constitutes what we call the Kirchhoff relation. An equivalent relation would give the variation of the heat of transformation at constant volume with the temperature as a function of the molar specific heat capacity at constant volume associated with the transformation. 

The term A C is linked to the molar specific heat capacities at constant pressure in the reference conditions of all the components of the reaction by the expression [4.6] ... 

If we consider a substance undergoing an allotropic transformation in the solid state at temperature T, which melts at temperature 7> and boils at temperature Tsb, to integrate expressions [4.4] and [4.6], it is necessary to divide the temperature interval between the initial temperature To and the temperature T into slices. Each slice is characterized by a phase and therefore a function of the molar specific heat capacity at constant pressure with changing temperature. Thus, integration of equation [4.4] involves two t3 es of terms ... 

By combining all these relations, we can also obtain an expression which links the equilibrium constant at a temperature T to a value of that constant at a different To, and the variations of the molar specific heat capacities in each temperature interval defined. We finally find a relation of the type ... 

If we know the enthalpy at a temperature To, it is easy to use a relation such as [4.7] to calculate that enthalpy at any temperature T, provided we know the variations of the molar specific heat capacities of the reaction components between temperatures To and T and the enthalpies of state change of those components within that temperature range. 

Cp and Cp respectively denote the specific mass heat of the sample and its molar specific heat capacity at constant pressure m is its mass and M the molar mass of the substance in question. We can write the following for the flux ... 

These temperatures are determined on the basis of the vibration frequencies of the bonds calculated on the basis of the spectral data. Remember that the molar specific heat capacity of a solid tends toward zero as its temperature tends toward absolute zero (with the entropy tending toward a constant). 

Cj3 molar specific heat capacity of the distillate J-kmol" °C ... 

Cp Molar specific heat capacity at constant pressure, in JK mol ... 

This expression will be used later on when we are calculating the contribution of the free electrons to the molar specific heat capacity of the metal at constant volume (see section 1.8.2.1). However, in order to do that, we need to know the term , which is the number of free electrons per atom of the metal. Sommerfeld s model does not provide us with this number, but Brillouin s band theory, or zone theory, can be used to evaluate it. 

Molar specific heat capacities of crystalline solids... 

At high temperature, the molar specific heat capacity is reduced to ... 

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