Hello.
http : webbook.nist.gov. is a good online data bank for material properties. I have checked a few heat capacities of materials on that. The general form of formula is as follow: Cp° = A + B*t + C*t2 + D*t3 + E/t2 Cp° is heat capacity (J/mol*K) t is temperature (K) / 1000 A, B, C, D and E are constants and given in table according to range of temperature for example : for Fe2O3, there are 3parts of temperature that make 3 groups of constants( A, B, C, D and E ) and 3groups of heat capacities that aren't continuous compared to each other. is it correct to calculate this parameter discontinuous? what is the reason? the figure of result is attached below. Thank you.
Hello Ensiyeh Karimi ,
Discontinuities in the heat capacity curve of a compound are caused by a phase change or transition. Because heat capacity is defined at a thermal equilibrium state, but actually measured at a nonequilibrium thermal state, due to the necessity of raising the temperature of the sample by injecting heat into it, heat capacity is a difficult measurement to make. Very few textbooks even explain how the measurement is actually done, see [1] for a good explanation. The heat capacity at a phase change or transition is even more uncertain due to the dynamics of the phase change. Hence, in the case of your compound, there are three separate tables bracketting the two phase change temperatures, i.e., the heat capacity is measured up to [or down to] but excluding a temperature region surrounding the phase change temperature. What you are doing is, in my opinion, absolutely okay.
[1] Mark W. Zemansky, Richard H. Dittman; Heat and Thermodynamics; McGraw-Hill Inc.; 1981; pp. 78-82.
Regards,
Tom Cuff
Basically the answer by Thomas Cuff is correct.
But as a physicist I would rather say "Discontinuities in the heat capacity curve of a compound are due to a phase change or transition"; the physical cause is that the effects for heat storage in the different phases are different. Heat storage is affected by how particles can move, and in the solid phase this is very different than in the liquid phase, and again completely different in the gas phase. This is why there are discontinuities when the phase changes, and usually only gradual changes within the same phase.
Regards,
Harald
Hello Harald Mehling ,
According to Websters' Seventh New Collegiate Dictionary, G. & C. Merriam Company, 1965, the phrase "due to" means "attributable, ascribable", i.e. "capable of being attributed", or using just the verb intransitive "attribute", it means "to explain by way of cause". I suppose this is an example of what Wittengenstein meant by the aphorism "The limits of my language means the limits of my world." But I do agree that the cause of a phase is mysterious of and by itself. You do not get a phase with 1 mole of atoms with each atom 1 meter from its closest neighbors. The atoms must be close enough and numerous enough to where their interactions with one another cannot be ignored. Only then do they form a phase. But why do some atoms and some molecules form so many phases? For example, Laughlin [1] mentions that ordinary ice has, at last count, some 11 different crystalline phases.
[1] Robert B. Laughlin; A Different Universe; Basic Books; 2005; p. 35, see also endnote 3 for Chapter 4 on p. 227.
Regards,
Tom Cuff
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