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Miscellaneous Problems in Specific Heats

  • E. S. R. Gopal
Part of the The International Cryogenics Monograph Series book series (INCMS)

Abstract

In the previous chapters, various aspects of specific heats of solids, liquids, and gases have been discussed. It is a common experience to find that two phases can coexist over a range of pressure and temperature. Consider, for instance, water and its vapor contained in a vessel of volume V. If the temperature is raised slightly, a small quantity of water is converted into steam, absorbing latent heat in the process, and a new equilibrium pressure is established. In a P-T plane (Fig. 8.1), this will be represented as an equilibrium curve. Quantities such as the density, specific heat, and compressibility remain finite but different in the two phases. An interesting relation among the thermodynamic quantities at such an equilibrium curve is furnished by the Clausius-Clapeyron equation. To derive this, apply Maxwell’s relation (∂P/∂T) υ = (∂S/∂V) T [equation (1.11)] to the system. The latent heat L12 is equal to T dS at the phase boundary, and so
$$\frac{{DP}}{{DT}} = \frac{{{S_2} - {S_1}}}{{{V_2} - {V_1}}} = \frac{{{L_{12}}}}{{T({V_2} - {V_1})}}$$
(8.1)
where D/DT stands for the derivative along the equilibrium curve. This simple equation, in which all the quantities can be determined experimentally, forms a rigorous practical test of the first and second laws of thermodynamics.

Keywords

Latent Heat Natural Rubber Equilibrium Curve Vitreous Silica Debye Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Plenum Press 1966

Authors and Affiliations

  • E. S. R. Gopal
    • 1
  1. 1.Department of PhysicsIndian Institute of ScienceBangaloreIndia

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