Solid specific heat capacity

Gases Molar Heat Capacities (cal deg moT ) Liquids Molar Heat Capacities (cal deg" mol ) Solids Specific Heat Capacities (cal deg g )... 

The heat capacity of a subshince is defined as the quantity of heat required to raise tlie temperature of tliat substance by 1° the specific heat capacity is the heat capacity on a unit mass basis. The term specific heat is frequently used in place of specific heat capacity. This is not strictly correct because traditionally, specific heal luis been defined as tlie ratio of the heat capacity of a substance to the heat capacity of water. However, since the specific heat of water is approxinuitely 1 cal/g-°C or 1 Btiiyib-°F, the term specific heal luis come to imply heat capacity per unit mass. For gases, tlie addition of heat to cause tlie 1° tempcniture rise m iy be accomplished either at constant pressure or at constant volume. Since the mnounts of heat necessary are different for tlie two cases, subscripts are used to identify which heat capacity is being used - Cp for constant pressure or Cv for constant volume. Tliis distinction does not have to be made for liquids and solids since tliere is little difference between tlie two. Values of heat capacity arc available in the literature. ... 

The high-temperature contribution of vibrational modes to the molar heat capacity of a solid at constant volume is R for each mode of vibrational motion. Hence, for an atomic solid, the molar heat capacity at constant volume is approximately 3/. (a) The specific heat capacity of a certain atomic solid is 0.392 J-K 1 -g. The chloride of this element (XC12) is 52.7% chlorine by mass. Identify the element, (b) This element crystallizes in a face-centered cubic unit cell and its atomic radius is 128 pm. What is the density of this atomic solid ... 

Assuming plug flow of the gas and complete mixing of the solids, calculate the coefficient for heat transfer between the particles and the gas. The specific heat capacity of air is 0.85 kJ/kg K. 

A single-effect evaporator is used to concentrate 7 kg/s of a solution from 10 to 50 per cent of solids. Steam is available at 205 kN/m2 and evaporation takes place at 13.5 kN/m2. If the overall heat transfer coefficient is 3 kW/m2 K, calculate the heating surface required and the amount of steam used if the feed to the evaporator is at 294 K and the condensate leaves the heating space at 352.7 K. The specific heat capacity of a 10 per cent solution is 3.76 kJ/kgK, the specific heat capacity of a 50 per cent solution is 3.14 kJ/kgK. 

Solids (per cent by mass) Boiling-point rise (deg K) Specific heat capacity (kJ/kg K) Heat of dilution (kJ/kg)... 

A liquor containing 15 per cent solids is concentrated to 55 per cent solids in a doubleeffect evaporator operating at a pressure of 18 kN/m2 in the second effect. No crystals are formed. The feedrate is 2.5 kg/s at a temperature of 375 K with a specific heat capacity of 3.75 kJ/kg K. The boiling-point rise of the concentrated liquor is 6 deg K and the pressure of the steam fed to the first effect is 240 kN/m2. The overall heat transfer coefficients in... 

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. 

A flow of 0.35 kg/s of a solid is to be dried from 15 per cent to 0.5 per cent moisture on a dry basis. The mean specific heat capacity of the solids is 2.2 kJ/kgdegK. It is proposed that a co-current adiabatic dryer should be used with the solids entering at 300 K and, because of the heat sensitive nature of the solids, leaving at 325 K. Hot air is available at 400 K with a humidity of 0.01 kg/kg dry air and the maximum allowable mass velocity of the air is 0.95 kg/m2s. What diameter and length should be specified for the proposed dryer ... 

We can then solve this equation for the specific heat capacity of the solid. 

From the steam tables in the Appendix, the latent heat of vaporisation of water at 312 K is 2410 kl/kg. Again from steam tables, the specific heat capacity of water vapour = 1.88 kJ/kg K and that of the solids will be taken as 2.18 kl/kg K. 

Solids concentration Boiling point rise Specific heat capacity Heat of dilution... 

A triple-effect evaporator is fed with 5 kg/s of a liquor containing 15 per cent solids. The concentration in the last effect, which operates at 13.5 kN/m2, is 60 per cent solids. If the overall heat transfer coefficients are 2.5, 2.0 and 1.1 kW/m2 K, respectively, and the steam is fed at 388 K to the first effect, determine the temperature distribution and the area of heating surface required in each effect, assuming the calandrias are identical. What is the economy and what is the heat load on the condenser The feed temperature is 294 K and the specific heat capacity of all liquors is 4.18 kJ/kg K... 

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. 

Cps specific heat capacity of solid phase at constant pressure... 

Figure 11.7 Calculation of TD24 as a function of the temperature at which the detection limit of lOWkg-1 is reached with different values of the activation energy of 50 kj mol-1 (solid line) 75, 100, and 150kjmof (dashed lines) and a specific heat capacity of 1 kjkg 1 K 1. The dotted line represents the 100 K-rule. ...

The instrument software can be used to derive properties of the sample from the thermogram data. These may include specific heat capacity, temperature of transition, heat of transition, solid fat content and reaction kinetics constants. 

In general a polymer sample is neither completely crystalline nor completely amorphous. Therefore, in the temperature region between Tg and Tm the molar heat capacity follows some course between the curves for solid and liquid (as shown in Fig. 5.1 for 65% crystalline polypropylene). This means that published single data for the specific heat capacity of polymers should be regarded with some suspicion. Reliable values can only be derived from the course of the specific heat capacity as a function of temperature for a number of samples. Outstanding work in this field was done by Wunderlich and his co-workers. Especially his reviews of 1970 and 1989 have to be mentioned here. 

With the aid of Eqs. (5.7) and (5.8) the specific heat capacity in the solid and the liquid state at temperatures of practical interest may be predicted approximately from their values at room temperature. 

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