# Specific-heat Sentence Examples

Weber showed that the

**specific heat**increases rapidly with increasing temperature.The density of solid sulphur is 2 062 to 2'070, and the

**specific heat**0.1712; it is a bad conductor of electricity and becomes negatively electrified on friction.It is of course in such a case necessary to know the

**specific heat**of the liquid in the calorimeter.In the more complex gases the

**specific heat**varies considerably with temperature; only in the case of monatomic gases does it remain constant.He regarded these anomalies as solely due to the chemical nature of the elements, and ignored or regarded as insignificant such factors as the state of aggregation and change of

**specific heat**with temperature.AdvertisementSince the atomic heat of the same element varies with its state of aggregation, it must be concluded that some factor taking this into account must be introduced; moreover, the variation of

**specific heat**with temperature introduces another factor.We now proceed to discuss molecular heats of compounds, that is, the product of the molecular weight into the

**specific heat**.The

**specific heat**of a compound may, in general, be calculated from the specific heats of its constituent elements.The

**specific heat**of indium is o 057; and the atomic heats corresponding to the atomic weights 38, 76 and 114 are 3.2, 4.3, 6.5.The density and

**specific heat**of the tetragonal form are greater than those of the yellow.AdvertisementLavoisier he made an important series of experiments on

**specific heat**(1782-1784), in the course of which the "ice calorimeter" was invented; and they contributed jointly to the Memoirs of the Academy (1781) a paper on the development of electricity by evaporation.Laplace's treatise on

**specific heat**was published in German in 1892 as No.In physical chemistry he carried out many researches on the nature and process of solution, investigating in particular the thermal effects produced by the dilution of saline solutions, the variation of the

**specific heat**of saline solutions with temperature and concentration, and the phenomena of liquid diffusion.The

**specific heat**is 0.09555 (Regnault).The heat evolved in this process may be represented by s"(o' - o"), where s" is the

**specific heat**of the substance in the second state at saturation pressure.AdvertisementThe whole quantity of heat required to raise the temperature from 0" to 0' at constant pressure along the path EC is H+h, which is equal to S(0' - o"), where S is the

**specific heat**at constant pressure.The value of the

**specific heat**s at constant volume can also be measured in a few cases, but it is generally necessary to deduce it from that at constant pressure, by means of relation (6).A similar expression for the variation of the

**specific heat**S at constant pressure is obtained from the second expression in (8), by taking p and 0 as independent variables; but it follows more directly from a consideration of the variation of the function (E+pv).The values of the corresponding functions for the liquid or solid cannot be accurately expressed, as the theoretical variation of the

**specific heat**is unknown, but if we take the**specific heat**at constant pressure s to be approximately constant, and observe the small residual variation dh of the total heat, we may write F'=s'D+dh+B'.Its

**specific heat**is between 0.0298 (Dulong and Petit) and 0.03244 (Regnault).AdvertisementAccording to Thoulet and Chevallier the

**specific heat**diminishes as salinity increases, so that for io per mille salinity it is o 968, for 35 per mille it is only o 932, that of pure water being taken as unity.On account of the high

**specific heat**of sea-water the diurnal range of temperature at the surface is very small.If the volume of the gas is kept constant, we put dv=o in equation (18) and dQ = JC0NmdT, where C v is the specific

**Specific heat**of the gas at constant volume and J is the mechanical equivalent of heat.If a solid body is regarded as an aggregation of similar atoms each of mass m, its

**specific heat**C is given, as in formula (19) by C = i (n+3) R/Jm.Its specific gravity is 21.3-22.48 (Deville and Debray) and its

**specific heat**is 0.03113 (Regnault).AdvertisementThe

**specific heat**of iodine vapour at constant pressure is o-03489, and at constant volume o 02697.Closely associated with the effect of continental immobility are the effects dependent on the low

**specific heat**and the opacity of the lands, in contrast with the high**specific heat**and partial transparence of the ocean waters.With a guess at the

**specific heat**we might then calculate the maximum temperature to which the substance might be raised, if there were no loss by radiation or otherwise.The probable error in neglecting any variation of

**specific heat**is small, and we may calculate L from the values of Lo - (s - s') (To - T), where s - s' is about 0.5 calories.Recently Hermann Walther Nernst has been able to deduce the transitionpoint in the case of sulphur from the

**specific heat**and the heat developed in the transition only.The advantage is that the quantities of heat are measured directly in absolute measure, in terms of the current, and that the results are independent of a knowledge of the

**specific heat**.It is a malleable metal, of specific gravity 1.64 (Nilson and Pettersson) and a

**specific heat**of 0.4079.Its

**specific heat**is 0.1946.Its specific gravity is 6.739, and its

**specific heat**0.0877.The

**specific heat**of a substance is sometimes defined as the thermal capacity of unit mass, but more often as the ratio of the thermal capacity of unit mass of the substance to that of unit mass of water at some standard temperature.But the

**specific heat**of water is often stated in terms of other units.In any case it is necessary to specify the temperature, and sometimes also the pressure, since the

**specific heat**of a substance generally depends to some extent on the external conditions.This is a very good method of comparing the mean specific heats over two ranges of temperature such as 0-50, and 50-100, or 0-20 and 20-40, but it is not so suitable as the electric method described below for obtaining the actual

**specific heat**at any point of the range.A common example of this method is the determination of the

**specific heat**of a liquid by filling a small calorimeter with the liquid, raising it to a convenient temperature, and then setting it to cool in an enclosure at a steady temperature, and observing the time taken to fall through a given range when the conditions have become fairly steady.The method requires very delicate weighing, as one calorie corresponds to less than two milligrammes of steam condensed; but the successful application of the method to the very difficult problem of measuring the

**specific heat**of a gas at constant volume, shows that these and other difficulties have been very skilfully overcome.The Absolute Value Of The

**Specific Heat**Deduced Necessarily Depends On The Absolute Values Of The Electrical Standards Employed In The Investigation.But For The Determination Of Relative Values Of Specific Heats In Terms Of A Standard Liquid, Or Of The Variations Of

**Specific Heat**Of A Liquid, The Method Depends Only On The Constancy Of The Standards, Which Can Be Readily And Accurately Tested.The

**Specific Heat**Itself Can Be Deduced Only By Differentiating The Curve Of Observation, Which Greatly Increases The Uncertainty.This quantity is now, as the result of further experiments, added to the values of h, and also represented in the formula for the

**specific heat**itself by the cubic term.But This Is Really Of No Consequence, Since The

**Specific Heat**At Constant Volume Cannot Be Practically Realized.It Was Proposed By A Committee Of The British Association To Select The Temperature At Which The

**Specific Heat**Was 4.20O Joules, Leaving The Exact Temperature To Be Subsequently Determined.In The Case Of Solids And Liquids Under Ordinary Conditions Of Pressure, The External Work Of Expansion Is So Small That It May Generally Be Neglected; But With Gases Or Vapours, Or With Liquids Near The Critical Point, The External Work Becomes So Large That It Is Essential To Specify The Conditions Under Which The

**Specific Heat**Is Measured.The Well Known Experiments Of Regnault And Wiedemann On The

**Specific Heat**Of Gases At Constant Pressure Agree In Showing That The Molecular**Specific Heat**, Or The Thermal Capacity Of The Molecular Weight In Grammes, Is Approximately Independent Of The Temperature And Pressure In Case Of The More Stable Diatomic Gases, Such As 112,02, N2, Co, &C., And Has Nearly The Same Value For Each Gas.The Direct Determination Of The

**Specific Heat**At Constant Volume Is Extremely Difficult, But Has Been Successfully Attempted By Joly With His Steam Calorimeter, In The Case Of Air And C02.Employing Pressures Between 7 And 27 Atmospheres, He Found That The

**Specific Heat**Of Air Between 10 And Ioo C. Increased Very Slightly With Increase Of Density, But That Of Co 2 Increased Nearly 3% Between 7 And 21 Atmospheres.If The Molecules Are Supposed To Be Like Smooth, Hard, Elastic Spheres, Incapable Of Receiving Any Other Kind Of Energy Except That Of Translation, The

**Specific Heat**At Constant Volume Would Be The Increase Per Degree Of The Kinetic Energy Namely 3Pv/20=3R/2, That At Constant Pressure Would Be 5R/2, And The Ratio Of The Specific Heats Would Be 5/3 Or 1.666.For Such Gases, Assuming A Constant Ratio Of Rotation To Translation, The

**Specific Heat**At Low Pressures Would Be Very Nearly Constant.The Experimental Evidence, However, Is Somewhat Conflicting, And Further Investigations Are Very Desirable On The Variation Of

**Specific Heat**With Temperature.Given The

**Specific Heat**As A Function Of The Temperature, Its Variation With Pressure May Be Determined From The Characteristic Equation Of The Gas.No Doubt There Must Be Approximate Relations Between The Atomic And Molecular Heats Of Similar Elements And Compounds, But Considering The Great Variations Of

**Specific Heat**With Temperature And Physical State, In Alloys, Mixtures Or Solutions, And In Allotropic Or Other Modifications, It Would Be Idle To Expect That The**Specific Heat**Of A Compound Could Be Accurately Deduced By Any Simple Additive Process From That Of Its Constituents.If the saturated vapour behaves as a perfect gas, the change of intrinsic energy E depends only on the temperature limits, and is equal to s (8-00), where s is the

**specific heat**at constant volume.The ideal method of determining by direct experiment the relation between the total heat and the

**specific heat**of a vapour is that of Joule and Thomson, which is more commonly known in connexion with steam as the method of the throttling calorimeter.From a different point of view, equation (12) may be applied to determine the

**specific heat**of steam in terms of the rate of variation of the total heat.The method of deducing the

**specific heat**from Regnault's formula for the variation of the total heat is evidently liable in a greater degree to the objections which have been urged against his method of determining the**specific heat**, since it makes the value of the**specific heat**depend on small differences of total heat observed under conditions of greater difficulty at various pressures.The more logical method of procedure is to determine the

**specific heat**independently of the total heat, and then to deduce the variations of total heat by equation (52).The simplest method of measuring the

**specific heat**appears to be that of supplying heat electrically to a steady current of vapour in a vacuum-jacket calorimeter, and observing the rise of temperature produced.Later and more accurate experiments have confirmed the experimental value, and have shown that the limiting value of the

**specific heat**should consequently be somewhat smaller than that given by Maxwell's hypothesis.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.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.Taking for ice and water the following numerical data, L = 674.7, 6 74.7, L 1 =595.2, L r = 79.5, R = o 11 03 cal./deg., po = 4.61 mm., s-S = 519 cal./deg., and assuming the

**specific heat**of ice to be equal to that of steam at constant pressure (which is sufficiently approximate, since the term involving the difference of the specific heats is very small), we obtain the following numerical formulae, by substitution in (23), Ice..The close agreement found under these conditions is a very strong confirmation of the correctness of the assumption that a vapour at low pressures does really behave as an ideal gas of constant

**specific heat**.The approximate equation of Rankine (23) begins to be I or 2% in error at the boiling-point under atmospheric pressure, owing to the coaggregation of the molecules of the vapour and the variation of the

**specific heat**of the liquid.Omitting w and neglecting the small variation of the

**specific heat**of the liquid, the result is simply the addition of the term (c-b)/V to formula (23) log p=A+B/B - I - C log B-f-(c-b)IV..The most uncertain data are the variation of the

**specific heat**of the liquid and the value of the small quantity b in the formula (13).The effect of variation of the

**specific heat**is more important, but is nearly eliminated by the form of the equation.It is equivalent, as Callendar (loc. cit.) points out, to supposing that the variation of the

**specific heat**is due to the formation and solution of a mass w/(v-w) of vapour molecules per unit mass of the liquid.The values of the

**specific heat**in the next column are calculated for a constant pressure equal to that of saturation by formula (16) to illustrate the increase of the**specific heat**with rise of pressure.The

**specific heat**at any given pressure diminishes with rise of temperature.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**.Its

**specific heat**is 0.05701 (Regnault) or 0.0559 (Bunsen); its coefficient of linear expansion is 0.0000-1921.The specific gravity of selenium is 4.8; the

**specific heat**varies from 0.0716 to 0.1147, depending upon the particular form.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.For some years after his appointment he devoted himself specially, with Francois Marcet (1803-1883), to the investigation of the

**specific heat**of gases, and to observations for determining the temperature of the earth's crust.From a series of elaborate experiments, Person deduced o 505 as the

**specific heat**of ice, or about half that of water.He succeeded a few years afterwards in verifying this remarkable prediction by the experimental demonstration that a current of positive electricity flowing from hot to cold in iron produced an absorption of heat, as though it possessed negative

**specific heat**in the metal iron.If the current flows from A to B there will be heat absorbed in AC and evolved in CB by the Thomson effect, if the

**specific heat**of electricity in AB is positive as in copper.If the quantity of heat absorbed and converted into electrical energy, when unit quantity of electricity (one ampere-second) flows from cold to hot through a difference of temperature, dt, be represented by sdt, the coefficient s is called the

**specific heat**of electricity in the metal, or simply the coefficient of the Thomson effect.For simplicity in the diagram the temperature gradient has been taken as uniform, and the

**specific heat**s= constant, but the total P.D.In this way the metal, owing to its high conductivity and low

**specific heat**as compared to that of water, is kept at a temperature far below its melting point if the water is renewed quickly enough.The enthalpy values were obtained by integrating the

**specific heat**capacity polynomial for each compound.In SI units the

**specific heat**capacity is the amount of heat required to raise 1 kg mass through 1 degree Kelvin.The enthalpy values were obtained by integrating the

**specific heat**polynomial for each compound.The presence of carbon dioxide tends to raise the lower limit since it has a higher

**specific heat**than nitrogen.His paper on the variation of the

**specific heat**with temperature, which appeared in 1907, was the first extension of Planck's fundamental hypothesis, and its verification in essentials is one of the most convincing arguments in its favour.A continuous flow calorimeter has been used by the writer for measuring quantities of heat conveyed by conduction (see Conduction Of Heat), and also for determining the variation of the

**specific heat**of water.The agreement of the values of H with those of Griffiths and Dieterici at low temperatures, and of the values of p with those of Regnault over the whole range, are a confirmation of the accuracy of the foregoing theory, and show that the behaviour of a vapour like steam may be represented by a series of thermodynamically consistent formulae, on the assumption that the limiting value of the

**specific heat**is constant, and that the isothermals are generally similar in form to those of other gases and vapours at moderate pressures.The

**specific heat**is.