Maximum heat capacity

The heat capacity is taken from the drop calorimetry of Dworkln and Bredig (384 to 1260 K) (6). Between 298 and 820 K, the observed enthalpy differences and the constraint of passing through zero at 298.15 K are fit by a linear least squares technique Cp = 15.99 + 6.22 X 10 T cal K" mol" (298-820 K). The heat capacity in the observed diffuse lambda transition region, 820-1100 K, was adjusted to properly reproduce the observed enthalpies. The sharp heat capacity maximum occurs at 1050 K (6) and... 

Low temperature heat capacities of ZnS0 (cr, o) have been measured by Weller ( ) from 51.7 - 296.5 K. A small heat capacity maximum was observed at 124.37 K. Our adopted value of S°(298.15 K) = 26.42+0.3 cal K mol obtained from C is based on S (51 K) = 2.27 cal K mol obtained by Weller (1 ) by extrapolation of the measured heat capacity with a combination of Debye and Einstein functions. We have smoothed the data of Weller (H)) by fitting the data with orthogonal polynomials over selected overlapping temperature intervals. 

The remaining titanate, Yb2Ti207 has proved to be enigmatic. While the earliest reports suggested LRO below 0.2 K from a sharp heat capacity maximum,recent studies of spin dynamics using both Mossbauer and juSR methods disclosed instead a discontinuous change in the spin fluctuation rate at that temperature, Figure 2.44.Subsequent neutron... 

Monte Carlo points. As the temperature is increased beyond the heat capacity maximum in the exact result, the MMC simulated points begin to rise but they are in poor agreement with the exact data. Additionally, the calculated error bars increase, but are artificially large in this calculation and do not accurately reflect the true asymptotic fluctuations of the heat capacity. Finally, at the highest calculated temperatures, both the Metropolis Monte Carlo and exact data are in agreement. 

This behaviour is characteristic of any two-state system, and the maximum in the heat capacity is called a Schottky anomaly. 

The thermal mass of parts and tools and the heating capacity of the autoclave naturally limit the maximum heating rate. Attempting to increase the heat-up rate by overheating the autoclave air can result in overheating of areas of the assembly with low thermal mass. 

Assuming that the maximum possible temperature difference is on the fluid side with the higher heat capacity rate, then... 

One of the more interesting results of these calculations is the contribution to the heat capacity. Figure 10.10 shows the temperature dependence of this contribution to the heat capacity for CH3-CCU as calculated from Pitzer s tabulation with 7r = 5.25 x 10-47 kg m2 and VQ/R — 1493 K. The heat capacity increases initially, reaches a maximum near the value expected for an anharmonic oscillator, but then decreases asymptotically to the value of / expected for a free rotator as kT increases above Vo. The total entropy calculated for this molecule at 286.53 K is 318.86 J K l-mol l, which compares very favorably with the value of 318.94T 0.6 TK-1-mol 1 calculated from Third Law measurements.7... 

The electronic contribution is generally only a relatively small part of the total heat capacity in solids. In a few compounds like PrfOHE with excited electronic states just a few wavenumbers above the ground state, the Schottky anomaly occurs at such a low temperature that other contributions to the total heat capacity are still small, and hence, the Schottky anomaly shows up. Even in compounds like Eu(OH)i where the excited electronic states are only several hundred wavenumbers above the ground state, the Schottky maximum occurs at temperatures where the total heat capacity curve is dominated by the vibrational modes of the solid, and a peak is not apparent in the measured heat capacity. In compounds where the electronic and lattice heat capacity contributions can be separated, calorimetric measurements of the heat capacity can provide a useful check on the accuracy of spectroscopic measurements of electronic energy levels. 

A vessel contains 1 tonm (I Mg) of a liquid of specific heat capacity 4.0 kj/kg K. The vessel is heated by steam at 393 K which is fed to a cod immersed in the agitated liquid and heat is lost to the surroundings at 293 K from the outside o." the vessel. How long dots it take to heat the liquid from 293 to 353 K and what is the maximum temperature to which the liquid can be heated When the liquid temperature has reached 353 K, the steam supply is tinned off for 2 hours (7.2 ks and the vessel cools. How long will it take to reheat the material to 353 K The surface area of the coil is 0 5 m2 and the overall coefficient of heat transfer to the liquid may be taken as 600 W/m2 K. The outside area of Lie vessel is 6 m2 and the coefficient of heat transfer to the surroundings may be taken as 10 W/m2 K. 

A reaction mixture is heated in a vessel fitted with an agitator and a steam coil of area 10 m2 fed with steam at 393 K. The heat capacity of the system is equal to that of 500 kg of water. The overall coefficient of heat transfer from the vessel of area 5 m2 is 10 W/m2 K. It takes 1800 s to heat the contents from ambient temperature of 293 to 333 K. How long will it take to heat the system to 363 K and what is the maximum temperature which can be reached ... 

To design the network for maximum energy recovery start at the pinch and match streams following the rules on stream heat capacities for matches adjacent to the pinch. Where a match is made transfer the maximum amount of heat. 

The maximum compression ratio (ratio of outlet to inlet pressure) for compressors depends on the design of the machine, the properties of the lubricating oil used in the machine, the ratio of heat capacities of the gas(Cp/Cy = y), other properties of the gas (e.g. tendency to polymerize when heated), and the inlet temperature. The most common types of compressor used for gas compression in the process industries are ... 

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