Heat capacity spikes

Fig. 15. Equilibrium heat capacity Cp versus T near 7],. The transition is first order and the latent heat is represented by a spike at 7 in C. We have used the free-volume parameters from Table II for 0.60KN03 0.40Ca(N03)2, To = 365.4°K, o To-416.8°K, and 0.0038. The other parameters chosen are I0 °K, o /co 1.1, 7 0, 0.15, a—0.3, A =...

The thermal conductivity of CO2 is illustrated in Figure 7. With increasing pressure, thermal conductivity increases at constant temperature. At constant pressure, thermal conductivity decreases with increasing temperature. Thermal conductivity exhibits a large (approximately seven-fold) spike near the critical point due to a similar increase in the constant-pressure heat capacity. Thermal conductivity is important for reactions for two main reasons. Depending on the heat of reaction, local hot (or cold) pockets could exist It is also important for the rapid heating and cooling necessary for some processes. 

It is obvious that properties such as isothermal compressibility, isobaric expansion coefficient and heat capacity, which display an extremum near the critical density, cannot be intermediate between those of vapor and liquid. As an example, we show in Figs. 4a and 4b the isobaric heat capacity of supercritical water along an Isobar. The sharp spike in Fig. 4a, with temperature as the abscissa, is the equivalent of the broad maximum in Fig. 4b, with density as abscissa. 

Figure 5.9 The Constant-Pressure Heat Capacity as a Function of Temperature at a First-Order Phase Transition. Because of the discontinuity in the entropy as a function of temperature, there is an infinite spike in the heat capacity at the phase transition.

Figure 5.13 The Heat Capacity of Helium Near the Lambda Transition. The heat capacity appears to become infinite, as in a first-order phase transition, but it rises smoothiy instead of showing a spike at one point as does a first-order phase transition.

Furthermore, in some materials other energy-absorptive processes occur at specific temperatures—for example, the randomization of electron spins in a ferromagnetic material as it is heated through its Curie temperature. A large spike is produced on the heat capacity-versus-temperature curve at the temperature of this transformation. 

Figure 11 Quasi-isothermal crystallization of polyamide 12 at 7 o=173°C, fp = 600s, ytr=0-5K. (a) Temperature profile consisting of an asymmetric sawtooth profile. The resulting heating rate and the heat flow rate show sharp spikes containing a broad spectrum of higher harmonics. (b) Specific reversing heat capacity as a function of time for different frequencies as indicated in the graph. The lines labeled Cp and Cp c indicate the data for liquid and crystalline polyamide 12 at 173 °C available from the ATHAS-DB, respectively. The used temperature time profile for sample preparation and crystallization is shown in the inset. Reproduced with permission from Schick, C. Anal. Bioanal. Chem. 2009, 395,1589-1611. ...

In this technique, an aliquot of sample (10 ml) is placed in a septum vial (20 ml) to a maximum of 50% capacity. The vial is spiked with surrogates and then heated for a moderate period ( 30 min) to create an equilibrium for volatile organic compounds between the air phase (headspace) and the water. The headspace is sampled (20—100 pi) with an airtight syringe and injected into a GC. Analytes are similar to... 

---