Title:

Verma Procedure for the Determination of Heat Capacity of Liquids

Authors:

Mahendra P. Verma

Key Words:

heat capacity, software

Conference:

Stanford Geothermal Workshop

Year:

2005

Session:

Geochemistry

Language:

English

Paper Number:

Verma

File Size:

1074KB

View File:

Abstract:

Recently, an ActiveX component, SteamTablesIIE, based on the IAPWS-95 formulation was written in Visual Basic 6.0 to calculate the thermodynamic properties of pure water as a function of any two independent state variables from temperature (T), pressure (P), volume (V), internal energy (U), enthalpy (H), and Gibbs free energy (G). However, it is found some thermodynamic inconsistencies which are the limitations for the functionality of SteamTablesIIE for all the ranges of the independent variables. For example, H=2000 kJ/kg for the 700 K isotherm is at P1=63.458 MPa and P2=456.356 MPa. If we consider T and H as independent variables, it is impossible to predict the correct values of P. Additionally, consider that there is a container filled with water at T=700 K. Since there is same H (2000 kJ/kg) for P=63.458 and P2=456.356 MPa, one can pressurize (from 63.458 to 456.356 MPa) the container without doing any work. In summary there is a violation of fundamental laws of thermodynamics for the H in the IAPWS-95 formulation.

The thermodynamic properties, U, H, G, and S are calculated from the experimental values of heat capacity at constant pressure (CP) and volume (CV). The measurements of CP for solid and CV for gases are feasible. However, it is impossible to measure CP or CV for all the values of T and P required for the calculation of the thermodynamic properties.

The reported experimental values of CP and CV along the saturation curve increase drastically near to the critical point of water. Similarly, the calculated value of CP or CV at the critical point calculated from the IAPWS-95 formulation is approximately 109 kJ/kg K, which means that the critical point acts as a heat sink. Additionally, the calculated values of the thermodynamic properties from CP or CV are not in agreement with the values obtained from the IAPWS-95 formulation.

The values of CP and CV have been measured along the saturation curve; however, their physical significance has never been explained. For example, there is need to know a relation between the increase in temperature and amount of heat given to a system at constant pressure in order to measure CP. However, there will be a change in pressure on changing temperature along the saturation curve. It means that it is not feasible to measure CP or CV along the saturation curve.

Till now, the thermodynamic properties have been calculated from CP and/or CV. As it has been discussed above that it is not possible to measure CP and CV of liquids at all conditions of independent variables (say T and P) required for calculating the thermodynamic properties. Therefore a new Verma procedure is devised. The heat capacity along the saturation curve, CSat is defined as the proportion of amount heat to the change in temperature. CSat is a function of only independent variable (say T).

Heat capacity is not a state function. Its value depends on the trajectory between two points. Therefore, one has to use the same trajectory for the calculation of the thermodynamic properties, U, H, G, S, etc. We are working to create new experimental data of the steam tables for pure water using this approach.


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