Heat capacity of solids and liquids

Figure 11.7 Experimental and calculated heat capacities of solid and liquid PTT [49], From Heat capacity of poly(trimethylene terephthalate), Pyda, M., Boiler, J., Grebowicz, J., Chuah, H., Lebedev, B. V. and Wunderlich, B., J. Polym. Sci., Polym. Phys. Ed., 36, 2499-2511 (1998), Copyright (1998 John Wiley Sons, Inc.). Reprinted by permission of John Wiley Sons, Inc...

Jones, W.M. and Giauque, W.F. The entropy of nitromethane. Heat capacity of solid and liquid. Vapor pressure, heats of fusion and vaporization, / Am. Chem. Soc., 69(5) 983-987, 1947. 

Calorimeters of Historical and Special Interest Around 1760 Black realized that heat applied to melting ice facilitates the transition from the solid to the liquid stale at a constant temperature. For the first time, the distinction between the concepts of temperature and heat was made. The mass of ice that melted, multiplied by the heal of fusion, gives the quantity of heal. Others, including Bunsen, Lavoisier, and Laplace, devised calorimeters based upon this principle involving a phase transition. The heat capacity of solids and liquids, as well as combustion heats and the production of heat by animals were measured with these caloritnelers. 

As with gases, data for the heat capacities of solids and liquids come from experiment. The temperature dependence of CP for solids and liquids can also be expressed by equations of the form of Eq. (4.4). Data for a few solids are given in Table 4.2, and for a few liquids, in Table 4.3. Data for specific heats (CP on a unit-mass basis) of many solids and liquids are given by Perry and Green.I... 

Molar heat capacity of solid and liquid polymers at 25°C ... 

Examination of the available literature data showed that, for all the polymers investigated, the curves for the molar heat capacity of solid and liquid might be approximated by straight lines, except for the solid below 150 K. So if the slopes of these lines are known, the heat capacity at an arbitrary temperature may be calculated approximately from its value at 298 K. For a number of polymers the slopes of the heat capacity curves, related to the heat capacity at 298 K, are mentioned in Table 5.3. 

As witli gases, tlie heat capacities of solids and liquids are found by experiment. Parameters for the temperature dependence of C/> as expressed by Eq. (4.4) are given for a few solids and hquids in Tables C.2 and C.3 of App. C. Correlationsfor tlie heat capacities of many solids and hquids are given by Periy and Green and by Daubert et al. ... 

J. S. Chickos, W. E. Acree, Jr. and J. F. liebman,./. Rhys. Chem. Ref. Data, 28, 1535 (1999). Strictly, use of these fusion enthalpies are estimates. The quantities should be corrected to 298 K from the melting point. However, the error is generally small because changes in heat capacities of solids and liquids as functions of temperature are generally small. 

The heat capacities of solids and liquids are also functions of temperature and independent of pressure. Data are given in Appendix A-.2, Physical Properties of Water A.3, Physical Properties of Inorganic and Organic Compounds and A.4, Physical Properties of Foods and Biological Materials. More data are available in (PI). 

The heat capacities of solid and liquid NbCls were also determined ... 

Applications of the Ice Calorimeter The very first applications of an ice calorimeter were reported by Lavoisier and Laplace (1780) (see Section 1.1.1). They measured the specific heat capacities of solids and liquids, as well as combustion heats and the production of heat by living animals. 

The worst simplification in Eq. 11.15 is the built-in assumption that A/isoUd to liquid is a constant, independent of temperature. Reference [18, p. 640] shows that if we do not make that simplification, but do assume that the heat capacities of solid and liquid are constant, independent of temperature, Eq. 11.15 becomes... 

SemicrystaUine samples show changes in the glass transition of the amorphous fraction which lead to a broadening of the transition range and shifts of the midpoint of the transition to higher temperature. In addition, the crystals may form a rigid—amorphous fraction, as described in the section about the heat capacities of solids and liquids at the beginning of this article on thermodynamic... 

A marginal but very important application of the drop calorimetric method is that it also allows enthalpies of vaporization or sublimation [162,169] to be determined with very small samples. The procedure is similar to that described for the calibration with iodine—which indeed is a sublimation experiment. Other methods to determine vaporization or sublimation enthalpies using heat flow calorimeters have been described [170-172], Although they may provide more accurate data, the drop method is often preferred due to the simplicity of the experimental procedure and to the inexpensive additional hardware required. The drop method can also be used to measure heat capacities of solids or liquids above ambient temperature [1,173],... 

Estimate the value of the heat capacity for solids and liquids. 

While we are discussing sofids, hquids, and gases we can consider the difference in heat capacities for solids and liquids. We will now need to use some of the information from the HUGA set of equations. Along the way we will repeat the case for an ideal gas and show where the derivation changes for the general case. We start from the definitions of C/> and Cy. 

The absolute value of the entropy of a compound is obtained directly by integration of the heat capacity from 0 K. The main contributions to the heat capacity and thus to the entropy are discussed in this chapter. Microscopic descriptions of the heat capacity of solids, liquids and gases range from simple classical approaches to complex lattice dynamical treatments. The relatively simple models that have been around for some time will be described in some detail. These models are, because of their simplicity, very useful for estimating heat capacities and for relating the heat capacity to the physical and chemical... 

Sections 3.1 and 3.2 describe heat capacity and explain how it may be determined at constant pressure Cp or at constant volume Cy. Most chemists need to make calculations with Cp, which represents the amount of energy (in the form of heat) that can be stored within a substance - the measurement having been performed at constant pressure p. For example, the heat capacity of solid water (ice) is 39 JK-1 mol-1. The value of Cp for liquid water is higher, at 75 JK-1 mol-1, so we store more energy in liquid water than when it is solid stated another way, we need to add more energy to H20(i) if its temperature is to increase. Cp for steam (H20(g)) is 34 JK-1 mol-1. Cp for solid sucrose (II) - a major component of any jam - is significantly higher at 425 JK-1 mol-1. 

If the assumption that the heat capacities of the pure liquid and solid A are equal is unwarranted, the expression for the standard free energy of fusion of A at T must be corrected ... 

Your task this time is to estimate the heat capacity of an unknown liquid. You have available a laboratory balance, a very well-insulated container, a sensitive thermometer that can measure liquid temperatures, and a thermocouple that can measure temperatures of solids. The container is a very poor conductor of heat, so that virtually all heat transferred to or from its contents goes entirely into changing the temperature of those contents. If you need anything else (within reason), you can get it. Devise as many ways as you can to estimate Cy, which you may assume is independent of temperature. [Example Mix in the insulated flask a known mass, mi, of your liquid at temperature T, and a known mass, m2, of hot water at temperature T2, and measure the final temperature Tf. Since you can calculate the heat lost by water, Q m2Cyw(T2 — Tf), and you know Q must also equal the heat gained by the other liquid, miCy(Tf Ti), you can solve for Cy.]... 

Since as we have already seen, the heat capacities of solids can be accounted for theoretically, it is of interest to examine whether the heat capacities of liquids can also be predicted in a similar way. We observe in the first place, that in the neighbourhood of the melting point the specific heats of simple solids and liquids are generally nearly equal. J Thus for solid mercury at 234 c = 6 77 cal./deg. mole, while for... 

Most of the equations for the heat capacities of solids, liquids, and gases are empirical. We usually express the heat capacity at constant pressure Cp as a function of temperature in a power series, with constants a, b, c, and so on for example. 

We now mention a few ways by which to estimate heat capacities of solids, liquids, and gases. For the most accurate results, you should employ actual experimental heat capacity data or equations derived from such data in your calculations. However, if experimental data are not available, there are a number of equations and estimation techniques that you may use which give estimates of values for the heat capacities. 

---