latent-heat

In the case of a solid or a liquid, the latent heat of isothermal expansion may often be neglected, and if the specific heat, s, be also taken as constant, we have simply 0-00 =s log e0/00.

In order to see whether the heat came out of the chips he compared the capacity for heat of the chips abraded by the boring bar with that of an equal quantity of the metal cut from the block by a fine saw, and obtained the same result in the two cases, from which he concluded that "the heat produced could not possibly have been furnished at the expense of the latent heat of the metallic chips."

If h is the water heat at the lower temperature, h l the water heat at the higher temperature, and L the latent heat at the higher temperature, the heat supply per pound of steam is equal to h1 - h2+L1, which, from the steam tables, with the values of the temperatures given, is equal to 1013 B.Th.U.

We can calculate the heat of formation from its ions for any substance dissolved in a given liquid, from a knowledge of the temperature coefficient of ionization, by means of an application of the well-known thermodynamical process, which also gives the latent heat of evaporation of a liquid when the temperature coefficient of its vapour pressure is known.

The latent heat of vaporization of mercury was found by Marignac to be 103 to 106.

These pans are sometimes heated by boiling oil, with the idea that under such conditions the sugar which is kept stirred all the time as it thickens cannot be burnt or caramelized; but the same object can be attained more economically with steam of a given pressure by utilizing its latent heat.

Moreover, his attention was engaged on studies which ultimately led to his doctrine of latent heat.

In 1764, with the aid of his assistant, William Irvine (1743-1787), he further measured the latent heat of steam, though not very accurately.

This doctrine of latent heat he taught in his lectures from 1761 onwards, and in April 1762 he described his work to a literary society in Glasgow.

In the notation of the calculus the relations become - dH/dp (0 const) = odv /do (p const) (4) dH/dv (0 const) =odp/do (v const) The negative sign is prefixed to dH/dp because absorption of heat +dH corresponds to diminution of pressure - dp. The utility of these relations results from the circumstance that the pressure and expansion co efficients are familiar and easily measured, whereas the latent heat of expansion is difficult to determine.

The heat absorbed in this change is called the latent heat of change of state, and may be represented by the symbol L'.

The loss of energy could not be greater than this on the simple kinetic theory, unless there were some evolution of latent heat of co-aggregation, due to the work done by the mutual attractions of the co-aggregating molecules.

L, Latent heat of fusion or vaporization.

If foodstuffs are to be employed it must be possible to grow them in excess of food requirements, and at a cost low enough to ensure that the price of the alcohol shall be about the same as that 1 The lower calorific value plus the latent heat of evaporation at constant volume.

The phase rule combined with the latent heat equation contains the whole theory of chemical and physical equilibrium.

First a small quantity of one of the pure components begins to crystallize out, and the rate of cooling is thereby diminished owing to the latent heat liberated by the change of state.

A familiar example is to be found in solutions of sodium sulphate, which may be cooled much below their saturation point and kept in the liquid state till a crystal of the hydrate Na 2 SO 4 IoH 2 O is dropped in, when solidification occurs with a large evolution of latent heat.

Then let us heat both ice and solution through the infinitesimal temperature range dT to the freezing point T of the solvent, melt the ice by the application of an amount of heat L, which measures its latent heat of fusion, and allow the solvent so formed to enter the solution reversibly through a semi-permeable wall into an engine cylinder, doing an amount of work Pdv.

units per unit concentration, L the latent heat as 79 4X 4.184 X Io 7 in the corresponding units, and dv the volume change in the solution for unit mass of solvent added we get for the quantity dT/c, where is the concentration of the solution, the value 1.857° C. per unit concentration.

where L, the latent heat of fusion, is the difference between the heats of evaporation for ice and water, and v is the specific volume of the vapour.

The latent heat L at any temperature is given by L=Lo - f 0 64 0 (s - s')dT, where Lo is value at To and s--s' is the difference in the specific heats of water and ice.

By an imaginary cycle of operations we may then justify the application to solutions of the latent heat equation which we have already assumed as applicable.

Its coefficient of linear expansion by heat is 0.0000222 (Richards) or 0.0000231 (RobertsAusten) per 1° C. Its mean specific heat between o° and ioo° is 0.227, and its latent heat of fusion loo calories (Richards).

By this means the latent heat of the steam, issuing from all pans but the last, is utilized for evaporating purposes, and from half to three-fourths of the fuel is saved.

The difficulties arise in connexion with the determination of the quantities of ice melted or steam condensed, and in measuring the latent heat of fusion or vaporization in terms of other units for the comparison of observations.

In the practical use of the instrument it is not necessary to know both the latent heat of fusion of ice and the change of volume which occurs on melting; it is sufficient to determine the change of volume per calorie, or the quantity of mercury which is drawn into the bulb of the apparatus per unit of heat added.

It is not possible to deduce a more satisfactory value from the latent heat and the change of density, because these constants are very difficult to determine.

The following are some of the values deduced by well-known experimentalists for the latent heat of fusion: - Regnault, 79.06 to 79.24 calories, corrected by Person to 79.43; Person, 79.99 calories; Hess, 80.34 calories; Bunsen, 80.025 calories.

Person and Hess avoided the error of water sticking to the ice by using dry ice at various temperatures below o° C., and determining the specific heat of ice as well as the latent heat of fusion.

8, January 1899) whether there may not be different modifications of ice with different densities, and different values of the latent heat of fusion.

The weight of steam condensed on the body gives a means of calculating the quantity of heat required to raise it from the atmospheric temperature up to ioo° C. in terms of the latent heat of vaporization of steam at zoo° C. There can be no appreciable gain or loss of heat by radiation, if the admission of the steam is sufficiently rapid, since the walls of the enclosure are maintained at too C., very nearly.

The application of the method appears to be practically limited to the measurements of specific heat between the atmospheric temperature and loo° C. The results depend on the value assumed for the latent heat of steam, which Joly takes as 536.7 calories, following Regnault.

Joly has himself determined the mean specific heat of water between 12° and zoo° C. by this method, in terms of the latent heat of steam as above given, and finds the result 9952.

(2) The Latent Heat Unit, Or The Quantity Of Heat Required To Melt Or Vaporize Unit Mass Of A Standard Substance Under Given Conditions.

For the depression of the freezing-point a relation of the same form applies, but do is negative, and L is the latent heat of fusion.

The quantity required per unit mass of the substance is termed the latent heat of vaporization.

The total heat of steam, for instance, is generally reckoned from the state of water at the freezing-point, o° C. If h denote the heat required to raise the temperature of the liquid from the selected zero to the temperature t° C., and if H denote the total heat and L the latent heat of the vapour, also at t° C., we have evidently the simple relation H =L+h..

The method commonly adopted in measuring the latent heat of a vapour is to condense the vapour at saturation-pressure in a calorimeter.

The quantity of heat so measured is the total heat of the vapour reckoned from the final temperature of the calorimeter, and the heat of the liquid h must be subtracted from the total heat measured to find the latent heat of the vapour at the given temperature.

Southern, was that the latent heat was constant.

Taking the difference between the values of H for any two temperatures 1 " Latent Heat of Steam," Phil.

The rate of change of the latent heat is easily deduced from that of the total heat by subtracting the specific heat of the liquid.

Since the specific heat of the liquid increases rapidly at high temperatures, while dH/d0 diminishes, it is clear that the latent heat must diminish more and more rapidly as the critical point is approached.

Regnault's formula for the total heat is here again seen to be inadmissible, as it would make the latent heat of steam vanish at about 870° C. instead of at 365° C. It should be observed, however, that the assumptions made in deducing the above formulae apply only for moderate pressures, and that the formulae cannot be employed up to the critical point owing to the uncertainty of the variation of the specific heats and the cooling effect Q at high pressures beyond the experimental range.

The empirical formulae above quoted must be compared and tested in the light of the theoretical relation between the latent heat and the rate of increase of the vapour-pressure (dp/d0), which is given by the second law of thermodynamics, viz.

The rate of variation of the latent heat at low pressures is equal to S-s, where s is the specific heat of the liquid.

103, p. 185, 1858) to represent the vapour-pressure of a solution, and was verified by Regnault's experiments on solutions of H 2 SO 4 in water, in which case a constant, the heat of dilution, is added to the latent heat.

and L 1 are the latent heats of vaporization of the solid and liquid respectively, the difference of which is equal to the latent heat of fusion L1.

A formula of the same type was given by Athenase Dupre (Theorie de chaleur, p. 96, Paris, 1869), on the assumption that the latent heat was a linear function of the temperature, taking the instance of Regnault's formula (io) for steam.

But this neglects the latent heat of solution, unless we may suppose it included by writing the internal latent heat L i in place of L in Callendar's formula.

The latent heat L (formula 9) is found by subtracting from H (equation 15) the values of the heat of the liquid h given in the same article.

Early in his career Cavendish took up the study of heat, and had he promptly published his results he might have anticipated Joseph Black as the discoverer of latent heat and of specific heat.

(21) where J is the dynamical equivalent of heat, L is the latent heat of unit of mass of the vapour, and p is the pressure.

We may call this the latent heat of surfaceextension.

Wolf that at ordinary temperatures the latent heat of extension of the surface of water is dynamically equivalent to about half the mechanical work done in producing the surface-extension.

Its specific gravity is 3.18828 (r), latent heat of fusion 16.185 calories, latent heat of vaporization 45.6 calories, specific heat 0.1071.

The extent of this loss is determined by the relation between the liquid heat and the latent heat of vaporization at the refrigerator temperature.

If r represents the latent heat of the vapour, and q 2 and q1 the amounts of heat contained in the liquid at the respective temperatures of T2 and T11 then the loss from the heat carried from the condenser into the refrigerator is shown by (q2-q1)/r and the useful refrigerating effect produced in the refrigerator is r-(q 2 -q i).

On the other hand, a great advantage is gained in the absorption machine by using the direct heat of the steam, without first converting it into mechanical work, for in this way its latent heat of vaporization can be utilized by condensing the steam in the coils and letting it escape in the form of water.

The binding energy of a second layer of adsorbate molecules is similar to the latent heat of sublimation or vaporization of the adsorbate molecules is similar to the latent heat of sublimation or vaporization of the adsorbate.

latent heat.

When surface meltwater refreezes internally, it releases huge amounts of latent heat thus softening the ice column.

Its latent heat of fusion is 11 7 calories, and its latent heat of vaporization is 23.95 calories (P. A.

The phase rule combined with the latent heat equation enables us to trace the general phenomena of equilibrium in solutions, and to elucidate and classify cases even of great complexity.

units per unit concentration, L the latent heat as 79 4X 4.184 X Io 7 in the corresponding units, and dv the volume change in the solution for unit mass of solvent added we get for the quantity dT/c, where is the concentration of the solution, the value 1.857Ã‚° C. per unit concentration.

Its coefficient of linear expansion by heat is 0.0000222 (Richards) or 0.0000231 (RobertsAusten) per 1Ã‚° C. Its mean specific heat between oÃ‚° and iooÃ‚° is 0.227, and its latent heat of fusion loo calories (Richards).

Person and Hess avoided the error of water sticking to the ice by using dry ice at various temperatures below oÃ‚° C., and determining the specific heat of ice as well as the latent heat of fusion.

The weight of steam condensed on the body gives a means of calculating the quantity of heat required to raise it from the atmospheric temperature up to iooÃ‚° C. in terms of the latent heat of vaporization of steam at zooÃ‚° C. There can be no appreciable gain or loss of heat by radiation, if the admission of the steam is sufficiently rapid, since the walls of the enclosure are maintained at too C., very nearly.

The application of the method appears to be practically limited to the measurements of specific heat between the atmospheric temperature and looÃ‚° C. The results depend on the value assumed for the latent heat of steam, which Joly takes as 536.7 calories, following Regnault.

Joly has himself determined the mean specific heat of water between 12Ã‚° and zooÃ‚° C. by this method, in terms of the latent heat of steam as above given, and finds the result 9952.

Assuming that the mean specific heat of water between 12Ã‚° and iooÃ‚° is really i o01 t in terms of the calorie at 20Ã‚° C. (see table, p. 638), the value of the latent heat of steam at iooÃ‚° C., as determined by Joly, would be 540.2 in terms of the same unit.

Griffiths Subsequently Applied The Same Method To The Measurement Of The Specific Heat Of Aniline, And The Latent Heat Of Va Orization Of Benzene And Water.

The total heat of steam, for instance, is generally reckoned from the state of water at the freezing-point, oÃ‚° C. If h denote the heat required to raise the temperature of the liquid from the selected zero to the temperature tÃ‚° C., and if H denote the total heat and L the latent heat of the vapour, also at tÃ‚° C., we have evidently the simple relation H =L+h..

Regnault's formula for the total heat is here again seen to be inadmissible, as it would make the latent heat of steam vanish at about 870Ã‚° C. instead of at 365Ã‚° C. It should be observed, however, that the assumptions made in deducing the above formulae apply only for moderate pressures, and that the formulae cannot be employed up to the critical point owing to the uncertainty of the variation of the specific heats and the cooling effect Q at high pressures beyond the experimental range.

Though no rise of temperature accompanies the melting of ice, there is yet a definite quantity of heat absorbed, namely, about 80 calories per gram; this is called the latent heat of fusion of water (see FusloN).

He understood that latent heat (as they say in physics) of patriotism which was present in all these men he had seen, and this explained to him why they all prepared for death calmly, and as it were lightheartedly.

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