Liquid-phase specific heat

Model parameters in fe — s model equations, dimensionless Model parameters in — Sc model equations, dimensionless Cp Liquid-phase specific heat, J/kg/K... 

The phase diagram for " He is shown in Fig. 4.3. There are two liquid phases, Hel and Hell, separated in the phase diagram by a line known as the lambda line (X line) and shown dashed in Fig. 4.3. The change that occurs at the X line is marked by a very characteristic anomaly in the specific heat capacity c of the liquid the specific heat capacity rises to a very high value at the lambda... 

Liquid- and Solid-Phase Specific Heat For an incompressible liquid or solid, the density is constant, so that... 

The integrated terms are simply the specific heat of the unit mass of adsorbent and its associated adsorbate. The specific heat at constant volume has been used for the adsorbate since, theoretically, there is no expansion of the adsorbate volume and the heat required to raise the temperature is the change in internal energy. In practice there will be some expansion and a pessimistically high estimate could use the specific heat at constant pressure The specific heat of the adsorbed phase is in any case difficult to estimate and it is common to approximate it to that of saturated liquid adsorbate at the same temperature. 

Here U = T — T )Cp/L is the appropriately rescaled temperature field T measured from the imposed temperature of the undercooled melt far away from the interface. The indices L and 5 refer to the liquid and solid, respectively, and the specific heat Cp and the thermal diffusion constant D are considered to be the same in both phases. L is the latent heat, and n is the normal to the interface. In terms of these parameters,... 

Equation (7) is an interesting example of the versatility of the hypothesistesting technique that Barnett has exploited. Thus, suppose it is assumed that the important fluid properties which control the burn-out phenomenon are density pL, specific heat, CPL, and thermal conductivity kL of the liquid phase, together with density of the vapor phase pv and the latent heat L Then, for burn-out in a uniformly heated round tube we have... 

The liquid phase reaction A - B is to be carried out in a plug flow tubular reactor at a constant pressure of 202.6 kPa. The feed is 600 kmoles/ksec of pure A with an inlet temperature of 200 °C. Pure A has a specific volume of 0.056 m3/kmole. The heat of reaction at 200 °C is —15 kJ/mole. The molar specific heats of A and B are both 42 J/mole-°K. The reaction rate constant in this range is given by the expression... 

Fig. 2.9. Specific heat of liquid 4He at temperature closed to its normal superfluid phase transition. 

Fig. 5.5. Per cent of remaining liquid 4He after pumping the bath down to the temperature T. Note the step around 2.2 K due to the transition to the superfluid phase with a peak in the specific heat... 

A liquid phase reaction, 2A = 2B, is conducted in a CSTR with 20% recycle through a heater as shown. Fresh input is at 300 K and consists of 500 kg/hr of water and 20 kgmol/hr of substance A. The recycle is at 350 K. Heat capacity of the solute is 40 kcal/gmol-K, the reaction is endothermic with AHr = +2000 cal/gmol of A converted, reactor volume is 25,000 liters and the specific rate is... 

Because the melting point of sodium metal is about 98° C (a bit lower than the boihng point of water), it is heated into a liquid phase and then transported in rail tank cars, where it cools and solidifies. When it arrives at its destination, heating coils in the tanks warm it back to the liquid stage, and it is then stored for use. Because sodium has a high specific heat rating, a major use is as a liquid coolant for nuclear reactors. Even though sodium (both solid and liquid) is extremely reactive with water, it has proven safe as a coolant for nuclear reactors in submarines. 

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