Isothermal latent heat

When an atom or molecule receives sufficient thermal energy to escape from a Hquid surface, it carries with it the heat of vaporization at the temperature at which evaporation took place. Condensation (return to the Hquid state accompanied by the release of the latent heat of vaporization) occurs upon contact with any surface that is at a temperature below the evaporation temperature. Condensation occurs preferentially at all poiats that are at temperatures below that of the evaporator, and the temperatures of the condenser areas iacrease until they approach the evaporator temperature. There is a tendency for isothermal operation and a high effective thermal conductance. The steam-heating system for a building is an example of this widely employed process. 

Pure vapor or substantially pure vapor can be considered condensed isothermally, and during the condensate range the latent heat of condensation is uniform. 

Latent heat The quantity of heat that is absorbed or released in an isothermal transformation of phase, in kj kg C b Latent heat of vaporization The heat added during an isothermal change of phase from liquid to gas. 

For example, in the case of the reversible isothermal transformation of ice to water at the melting point (273 K), the heat gained by the ice will be the latent heat of fusion (A//f = 6(X)6 J mol" ) and a corresponding quantity of heat will be lost by the surrounding, and... 

The theorem also applies to a heterogeneous system, such as a liquid in presence of its saturated vapour, or in presence of the solid. In the former case, vapour is liquefied by compression and gives out its latent heat. Under isothermal conditions this would escape as fast as produced, but if the heat is compelled to remain in the system, it raises the temperature and thereby increases the pressure. If, on the other hand, a mixture of ice and water is compressed, ice melts and the mass is cooled by abstraction of heat. If heat is allowed to enter from outside, so as to restore the original temperature, more ice melts, and the pressure falls by reason of the contraction. 

Transfer to the hot reservoir and expand isothermally till a mass m of liquid has been evaporated. The heat absorbed along BC is mLe where Le = latent heat of evaporation at T°. 

Thus, the isothermal is a straight line of slope [Cw(9 — On) + A] with respect to the humidity axis. At the reference temperature 90, the slope is X at higher temperatures, the slope is greater than X, and at lower temperatures it is less than X. Because the latent heat is normally large compared with the sensible heat, the slope of the isothermals remains positive down to very low temperatures. Since the humidity is plotted as the ordinate, the slope of the isothermal relative to the X-axis decreases with increase in temperature. When 9 > Bq and Jf > Jf0, the saturation humidity, the vapour phase consists of a saturated gas with liquid droplets in suspension. The relation between enthalpy and humidity at constant temperature 9 is ... 

It can be seen from Figure 13.5 that for the air-water system a straight line, of slope equal to the enthalpy of dry saturated steam (2675 kJ/kg), is almost parallel to the isothermals. so that the addition of live steam has only a small effect on the temperature of the gas. The addition of water spray, even if the water is considerably above the temperature of the gas, results in a lowering of the temperature after the water has evaporated. This arises because the. latent heat of vaporisation of the liquid constitutes the major part of the enthalpy of the vapour. Thus, when steam is added, it gives up a small amount of sensible heat to the gas, whereas when hot liquid is added a small amount of sensible heat is given up and a very much larger amount of latent heat is absorbed from the gas. 

A reboiler of a distillation column is required to supply 10 kg-s 1 of toluene vapor. The column operating pressure at the bottom of the column is 1.6 bar. At this pressure, the toluene vaporizes at 127°C and can be assumed to be isothermal. Steam at 160°C is to be used for the vaporization. The latent heat of vaporization of toluene is 344,000 J-kg 1, the critical pressure is 40.5 bar and critical temperature is 594 K. Steel tubes with 30 mm outside diameter, 2 mm wall thickness and length 3.95 m are to be used. The film coefficient (including fouling) for the condensing steam can be assumed to be 5700 Wm 2-K 1. Estimate the heat transfer area for ... 

Suppose we take a sample of bone-dry air at some temperature, Ti, and directly contact it with water until it becomes saturated at the same temperature. The water vapor that enters into the air contains with it its latent heat of vaporization. The vapor pressure of water out of the liquid will be greater than it is in the saturated air, causing vaporization to occur and subsequently increasing the humidity of the air-water-vapor mixture. The process of vaporization ends when the vapor pressure of the water in the air becomes equal to that of the liquid. At this condition the air is saturated. During the air saturation process, isothermal conditions for the water can be maintained if heat is supplied to replace the heat lost from it to the gas as latent heat of vaporization. Thus, heat transfer during the saturation of a gas with a liquid can be accomplished without a temperature differential (although this is rarely encountered). This type of heat transfer phenomenon, better known as diffusional heat transfer, is different from conduction, convection or radiation. 

If, rather, the hot fluid is an isothermally condensing vapor (such as steam), the latent heat duty is... 

The Latent Heats and Clapeyron s Equation.—There is a very important thermodynamic relation concerning the equilibrium between phases, called Clapeyron s equation, or sometimes the Clapeyron-Clausius equation. By way of illustration, let us consider the vaporization of water at constant temperature and pressure. On our P-V-T surface, the process we consider is that in which the system is carried along an isothermal on the ruled part of the surface, from the state whore it is all liquid, with volume Fz, to the state where it is all gas, with volume F . As we go along this path, we wash to find ihe amount of heat absorbed. We can find this from one of Maxwell s relations, Eq. (4.12), Chap. II ... 

According to Einstein, if the surface tension is a linear function of temperature, aQ=a—T(da/dT)—const., Mv=mo. vol., /,=intemal latent heat of evaporation, a=coefflcient of expansion, =isothermal compressibility, the following relations hold ... 

Creighton and Southern s law, 304 critical density, 46 heat, 318 isotherm, 360 point, 356 pressure, 100 solution temperature, 170 state, 352 temperature, 100, 102, 141 temperature, latent heat at, 339, 359, 365 volume, 26... 

Suppose, for example, that a substance is to be vaporized isothermally at 130 C, but the only available value of the heat of vaporization is at 80 C. A process path from the liquid at 130 C to the vapor at the same temperature must then be chosen that includes an isothermal vaporization step at 80 C specifically cool the liquid from 130 C to 80 C, vaporize the liquid at 80 C, and then heat the vapor back to 130°C. Summing the changes in enthalpy for each of these steps yields the change in enthalpy for the given process. (By definition, the calculated value is the latent heat of vaporization at 130 C.)... 

A supercooled liquid solidifies when inoculated with a small crystal of the solid, while the latent heat is evolved in the process. The solidification can be performed reversibly and made to yield work by evaporating the liquid at its vapour pressure allowing the vapour to expand isothermally until the pressure is equal to the vapour pressure of the solid, and then condensing to the solid state. 

Three different isothermal crystallization experiments were performed in this work classical static (i.e., quiescent) crystallization in the DSC apparatus, dynamic crystallization with the apparatus described above, and dynamic-static crystallization. Dynamic isothermal crystallization consisted in completely solidifying cocoa butter under a shear in the Couette apparatus. Comparison of shear effect with results from literature was done using the average shear rate y. This experiment did not allow direct measurement of the solid content in the sample. However, characteristic times of crystallization were estimated. The corresponded visually to the cloud point and to an increase of the cocoa butter temperature 1 t) due to latent heat release. The finish time, was evaluated from the temperature evolution in cocoa butter. At tp the temperature Tit) suddenly increases sharply because of the apparition of a coherent crystalline structure in cocoa butter. This induces a loss of contact with the outer wall and a sharp decrease in the heat extraction. 

This means that if the system is to maintain a constant temperature, the heat of reaction must be taken up by the heat of compression (or decompression). If the initial perturbation is an increase in pressure, then moderation will be observed only if the reaction induced in the system is such that the latent heat of decompression is supplied by the exothermicity of the reaction. The reaction must therefore be exothermal (hji j, negative), and at the same time be one in which the pressure decreases at constant volume pji y negative). If the reaction were endothermal, then isothermal conditions could only be maintained by a further increase in pressure. 

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