Molar heat capacity at constant pressure

Figure A2.5.2. Schematic representation of the behaviour of several thennodynamic fiinctions as a fiinction of temperature T at constant pressure for the one-component substance shown in figure A2.5.1. (The constant-pressure path is shown as a dotted line in figure A2.5.1.) (a) The molar Gibbs free energy Ci, (b) the molar enthalpy n, and (c) the molar heat capacity at constant pressure The fimctions shown are dimensionless...

When a substance is heated at constant pressure without change of phase through a temperature rise dr the heat absorbed is Cp dr, where Cp is the molar heat capacity at constant pressure, and the entropy increase is... 

Thus, for the ideal gas the molar heat capacity at constant pressure is greater than the molar heat capacity at constant volume by the gas constant R. In Chapter 3 we will derive a more general relationship between Cp m and CV m that applies to all gases, liquids, and solids. 

The temperature variation of the standard reaction enthalpy is given by Kirchhoff s law, Eq. 23, in terms of the difference in molar heat capacities at constant pressure between the products and the reactants. 

Calculate the standard entropy of vaporization of water at 85°C, given that its standard entropy of vaporization at 100.°C is 109.0 J-K -mol 1 and the molar heat capacities at constant pressure of liquid water and water vapor are 75.3 J-K -mol 1 and 33.6 J-K -mol, respectively, in this range. 

Figure 1.2 Molar heat capacity at constant pressure and at constant volume, isobaric expansivity and isothermal compressibility of AI2O3 as a function of temperature.

Figure 8.2 Molar heat capacity at constant pressure of H(g), H2(g) and H20(g). The open symbols at 5000 K represent the limiting classical heat capacity.

The measure of the energy input required for raising the temperature of a mole of solvent by a unit is the molar heat capacity (at constant pressure), Cp. 

Molar heat capacities at constant pressure for selected substances1... 

Cp = molar heat capacity at constant pressure 1 faraday, 2T = 96,500 coulombs per mole of electrons... 

So far only cp and Cp, the specific and the molar heat capacities at constant pressure, have been discussed. Obviously, these quantities are always dealt with in normal measurements. For the calculation of the specific heat capacity at constant volume, cv some relationships are available. An exact thermodynamic derivation leads to the equation ... 

Heat capacity, molar Heat capacity at constant pressure Heat capacity at constant volume Helmholtz energy Internal energy Isothermal compressibility Joule-Thomson coefficient Pressure, osmotic Pressure coefficient Specific heat capacity Surface tension Temperature Celsius... 

A similar argument is used to deal with s this is based on the empirical observation that in an adiabatic process involving a noble gas at low pressures, the product PV7 is virtually constant. Here 7 is a fixed quantity (which will later turn out to be the ratio of molar heat capacities at constant pressure and volume) whose exact significance is irrelevant at this stage near room temperature and for monatomic gases 7 has a value close to 5/3. We therefore use the product PV7 as a measure of the empirical entropy through the simple relation... 

Kirchhoff s equation), where is the molar heat capacity at constant pressure for species i at temperature T. 

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