Latent heat of volume change

Second—Having now the system at the final temperature value, suppose this to be kept constant, and let us consider that the pressure of the system is now allowed to rise by the amount dp. This involves an absorption of heat /dp, when t is the latent heat of pressure change (Naturally in this last process the volume must have changed concomitantly with the pressure) These two processes added together have been assumed to give the same total heat dQ For this case therefore we have—... 

A carefully studied example is the transition which takes place in liquidheliumat about 2.2 K. Theheat capacity and density of liquid helium as functions of the temperature are shown in Fig. 22. In this instance at least it is known that the two phases are able to co-exist, not merely at a particular temperature and pressure, but along a p-T equilibrium curve, as in the ordinary phase transitions already discussed. Similar effects are known to occur in many solids, notably in alloys, in the crystalline ammonium salts, in polymers and in solidified methane and hydrogen halides. For example, in ammonium chloride there is a sharp break in the heat capacity curve at —30.4 GL Now in any given example, if it were knotm with certainty that the latent heat and volume change were vanishingly small, the entropy... 

The entropy change AS/ - and the volume change AV/ - are the changes which occur when a unit amount of a pure chemical species is transferred from phase I to phase v at constant temperature and pressure. Integration of Eq. (4-18) for this change yields the latent heat of phase transition ... 

In addition to volume changes the effect of temperature is also important. Thus the specific latent heat of vaporization of a chemical is the quantity of heat, expressed as kJ/kg, required to change unit mass of liquid to vapour with no associated change in temperature. This heat is absorbed on vaporization so tliat residual liquid or tlie sunoundings cool. Alternatively an equivalent amount of heat must be removed to bring about condensation. Thus the temperature above a liquefied gas is reduced as tlie liquid evaporates and tlie bulk liquid cools. There may be consequences for heat transfer media and the strength of construction materials at low temperatures. 

Le — latent heat of evaporation. v2 — Vi = Ar = volume change accompanying unit mass of phase transition at the pressure p. 

Ni(C2HgN2)3(N03)2 is quite different - the space group type and the lattice change at (ca. 106 K). The transition show discontinuity of the cell volume and, as expected, there is a latent heat of transition. Notably at the critical temperature the two phases are structurally different and therefore they are in equilibrium at that temperature. A minor hysteresis is observed. 

The pf-relations of the six different forms of ammonium nitrate are illustrated diagrammatically in Eig. 85. M. Bellati and R. Romanese, and U. Behn measured the changes in volume at atm. press, at the four transition points. M. Bellati and R. Romanese have also measured the latent heats of the transformation... 

With motion along the connodal curve towards the plait-point, E and Ez, Si and S29 and Vi and Vz approach limits which may be called the energy, entropy, and volume in the critical. state, and the temperature and pressure also tend to limits which may be called the critical temperature and the critical pressure. Hence, in evaporation, the changes of volume and entropy, and the ext al work and latent heat of evaporation all tend to zero as the system approaches the critical state ... 

The equation, a direct consequence, or rather an expression, of the second law (as discussed on p. 26), has been repeatedly verified. In the first place it corresponds exactly to the law governing change of melting point with pressure, where q is the latent heat of fusion, v the increase of volume on fusion. And then Eeicher verified the above formula experimentally, while Mallard and Le Chatelier did the same for the conversion of silver iodide, which at 146° passes from hexagonal to regular. Eoozeboom, finally, has verified the equation for the fusion of the hydrate HBr.2H20 at — 11 3 which is due to chemical decomposition. 

The integral is the change of internal energy produced by the fusion of unit mass, or the internal latent heat of fusion w In general the difference between the total heat of fusion and w is a small quantity, as the change in volume on melting is very small. 

If we consider the melting point of a solid as a function of applied pressure, then we are more interested in the reciprocal of the coefficient in (14.4) i.e. in STjSp. This must be equal to TAfVjAfh where AfV and Afh are the volume change and latent heat of fusion respectively. If therefore we measure the volume change which accompanies melting and also the slope of the curve of m.p. against pressure, we can evaluate the latent heat of fusion Afh. 

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