Heat capacity at saturation

This equation may be applied to the calculation of the heat capacity of each of the two phases in a liquid-vapour system. These heat capacities are called the heat capacities at saturation. 

Differential scanning calorimetry studies of aqueous surfactant mixtures are typically measured in closed hollow containers or pans where the expansion of condensed phases causes only a minimal increase in pressure under these circumstances. Changes in pressure in surfactant-water systems resulting from the increase in water vapor pressure are typically small (a few atmospheres at most). In these cases, the measured heat capacities can be precisely defined as heat capacities at saturated vapor pressure [25], but usually they are numerically similar to those that would be obtained during constant pressure measurements [26] and so they are commonly taken as the latter. 

The heat capacity at saturation Cq(s or 1) is defined as the limit as Sr -> 0 of Wo/Sr where is the work which must be done (usually electrically) on the solid or liquid so as to raise its temperature by 8r in the presence of a vanishingly small amount of vapour, that is to say with the pressure varying with temperature along the (s + g) or (1 + g) saturation line. The quantity Co is usually more closely related to the quantity actually measured in modern heat-capacity calorimeters than the heat capacity at constant pressure C, to which it is related through the formula ... 

The liquid phase heat capacity values are derived from the enthalpy equation reported by Kenesbea et al. ( ). The equation is used for the region 478.9 - 600 K, i.e. that region in which the saturation heat capacity and the heat capacity at constant pressure are essentially the same in value. This equation is used also to extrapolate to 700 K and to an assumed glass transition temperature at 350 K. Below heat capacity values are those of the crystal. S (298.15 K) is... 

P = absolute pressure T — absolute temperature V = specific volume p = density = 1/F S = specific entropy H = specific enthalpy U = specific internal energy Cp — specific heat capacity at constarit pressure C = specific heat capacity at constant volume C(T = specific heat capacity at constant saturation W = velocity of sound fx = Joule-Thomson coefficient R = universal gas constant... 

Use data from the steam tables to calculate the heat capacity of saturated water vapor at 250 °C. 

From Tables 6 and 7 it follows that thermodynamic characteristics of Freon-20 at low pressures have been determined for gaseous and liquid phases and on the liquid-vapor saturation line. But the discrepancies among diverse groups of experimental data often exceed the error of measurement mentioned by the authors of the experimental work. This observation is addressed, in particular, to the experimental data about the second virial coefficient of equations of state (Fig. 1) and to the data about saturated vapor pressure. The agreement of experimental data for the heat capacity of saturated liquids is good, but the direct measurements were made at temperatures below the normal boiling point (T Bp = 334.3 K). The comparative analysis of experimental data about the ortho-baric density shows that the temperature dependence of density of the saturated liquid can be accepted with certainty in the interval from the triple point to the... 

Liquid Heat Capacity The two commonly used liqmd heat capacities are either at constant pressure or at saturated conditions. There is negligible difference between them for most compounds up to a reduced temperature (temperature/critical temperature) of 0.7. Liquid heat capacity increases with increasing temperature, although a minimum occurs near the triple point for many compounds. 

An initially clean activated carbon Led at 320 K is fed a vapor of benzene in nitrogen at a total pressure of 1 MPa. The concentration of benzene in the feed is 6 mol/m. After the Led is uniformly saturated with feed, it is regenerated using benzene-free nitrogen at 400 K and 1 MPa. Solve for Loth steps. For sim-phcity, neglect fluid-phase acciimiilation terms and assume constant mean heat capacities for stationary and fluid phases and a constant velocity. The system is described by... 

As an example of a negative heat capacity we have the specific heat of saturated steam. If unit mass of steam in the condition of saturation is raised one degree in temperature, and at the same time compressed so as to keep it just saturated at each temperature, it is found that heat is evolved, not absorbed, because the work spent in the compression exceeds the increase of intrinsic energy. 

A stirred reactor contains a batch of 700 kg reactants of specific heat 3.8 kJ/kg K initially at 290 K, which is heated by dry saturated steam at 170 kN/m2 fed to a helical coil. During the heating period the steam supply rate is constant at 0.1 kg/s and condensate leaves at the temperature of the steam. If heat losses arc neglected, calculate the true temperature of the reactants when a thermometer immersed in the material reads 360 K. The bulb of the thermometer is approximately cylindrical and is 100 mm long by 10 mm diameter with a water equivalent of 15 g, and the overall heat transfer coefficient to the thermometer is 300 W/m2 K. What would a thermometer with a similar bulb of half the length and half the heat capacity indicate under these conditions ... 

Distilled water is produced from sea water by evaporation in a single-effect evaporator working on the vapour compression system. The vapour produced is compressed by a mechanical compressor of 50 per cent efficiency, and then returned to the calandria of the evaporator. Extra steam, dry and saturated at 650 kN/m2, is bled into the steam space through a throttling valve. The distilled water is withdrawn as condensate from the steam space. 50 per cent of the sea water is evaporated in the plant. The energy supplied in addition to that necessary to compress the vapour may be assumed to appear as superheat in the vapour. Calculate the quantity of extra steam required in kg/s. The production rate of distillate is 0.125 kg/s, the pressure in the vapour space is 101.3 kN/m2, the temperature difference from steam to liquor is 8 deg K, the boiling-point rise of sea water is 1.1 deg K and the specific heat capacity of sea water is 4.18 kJ/kgK. 

A double-effect forward-feed evaporator is required to give a product which contains 50 per cent by mass of solids. Each effect has 10 m2 of heating surface and the heat transfer coefficients are 2.8 and 1.7 kW/m2 K in the first and second effects respectively. Dry and saturated steam is available at 375 kN/m2 and the condenser operates at 13.5 kN/m2. The concentrated solution exhibits a boiling-point rise of 3 deg K. What is the maximum permissible feed rate if the feed contains 10 per cent solids and is at 310 K The latent heat is 2330 kJ/kg and the specific heat capacity is 4.18 kJ/kg under all the above conditions. 

A salt solution at 293 K is fed at the rate of 6.3 kg/s to a forward-feed triple-effect evaporator and is concentrated from 2 per cent to 10 per cent of solids. Saturated steam at 170 kN/m2 is introduced into the calandria of the first effect and a pressure of 34 kN/m2 is maintained in the last effect. If the heat transfer coefficients in the three effects are 1.7, 1.4 and 1.1 kW/m2K respectively and the specific heat capacity of the liquid is approximately 4 kJ/kgK, what area is required if each effect is identical Condensate may be assumed to leave at the vapour temperature at each stage, and the effects of boiling point rise may be neglected. The latent heat of vaporisation may be taken as constant throughout. 

An evaporator, working at atmospheric pressure, is to concentrate a solution from 5 per cent to 20 per cent solids at the rate of 1.25 kg/s. The solution, which has a specific heat capacity of 4.18 kJ/kg K, is fed to the evaporator at 295 K and boils at 380 K. Dry saturated steam at 240 kN/m2 is fed to the calandria, and the condensate leaves at the temperature of the condensing stream. If the heat transfer coefficient is 2.3 kW/m2 K, what is the required area of heat transfer surface and how much steam is required The latent heat of vaporisation of the solution may be taken as being equal to that of water. 

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