Temperature-Averaged Specific Heats

If the temperature polynomial for each pure-component heat capacity is 

The results shown in Table 3-2 are obtained for the three gas-phase components in the reactor. 

Now that the pure-component heat capacities have been averaged over the temperature range of operation, it is necessary to focus on the conversion dependence of mass fractions and mole fractions. 

TABLE 3-2 Temperature-Averaged Pure-Component Heat Capacities for CO, H2, and CH3OH 

3-2 CONVERSION DEPENDENCE OF MASS FRACTION AND HEAT CAPACITY OF THE MIXTURE 

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In general, mole fractions are not linear functions of conversion because the total number of moles and the total molar flow rate are not constant when 5 = Vi 7 0. For this particular problem, 5 = —2. In summary, the easiest approach to performing a weighted average of heat capacities of all components in the mixture is to use a mass-fraction-weighted sum of the temperature-averaged specific heat of each pure component. Hence,... 

Extrusion blow moulding of bottles has been successfully accomplished in reeent years by attention to the points mentioned above. It is to be noted here that UP VC has a much lower average specific heat between the proeessing temperature and room temperature than polyethylene and, being essentially amorphous, no latent heat of fusion. This leads to much less heat needing to be removed on cooling of mouldings and very short cycle times are possible. 

Po = density of combustion products at initial temperature Tq Cp = average specific heat of mixture considered to be constant from Tq to maximum fireball temperature... 

Bhattacharya and Gedanken [11] have reported a template-free sonochemical route to synthesize hexagonal-shaped ZnO nanocrystals (6.3 1.2 nm) with a combined micro and mesoporous structure (Fig. 8.1) under Ar gas atmosphere. The higher porosity with Ar gas has been attributed to the higher average specific heat ratio of the Ar which leads to higher bubble collapse temperatures. With an intense bubble collapse temperature, more disorder is created in the product due to the incompleteness of the surface structure that led to greater porosity. Importance of gas atmosphere has been noted when the same process was carried out in the presence of air which results in the formation of ZnO without any porosity. 

The wetted surface area of the 2 m3 reactor during two-phase relief has been estimated as 8.6 m2. This is the full surface area of the bottom and the sides of the reactor because, if two-phase relief occurs, this whole area will be wetted inside the reactor with liquid. The heat input rate from the fire is estimated as 252 kW l For a closed reactor containing 793 kg of material, and using the average, specific heat capacity of 2.25 kJ/kg K, the effective rate of temperature rise due to the fire is given by ... 

The detonation temperature computed from the heat of explosion and from the average specific heat of the products must not exceed 1900°C for explosives intended for penetrating rock and 1500°C for those to be used in coal mines. 

Autoclave reactors are operated adiabatically, which means that the heat of reaction must be removed by the fresh ethylene entering the reactor. The conversion is related, therefore, to the difference in temperature between the feed and the reactor temperature. This limits the conversion to 15 - 20%. Taking into account the fact that the percentage conversion, Ax, can be approximated by using the average specific heat, cp, the enthalpy of the polymerization,... 

The heat capacity of a body is the amount of heat required to raise the temperature of that body 1K (1°C). For pure substances, it is most convenient to refer to quantities of molar heat capacity (heat capacity per mole) and, as discussed above, the specific heat capacity or, more commonly, the specific heat (heat capacity per unit of mass). As an example, the average specific heat of water is... 

A much greater heat quantity is involved in cooling the diamond from 550° C. to 90° K. The specific heat of diamond at 500° is about 0.4 cal./g. °C. and this decreases to only 0.0025 cal./g. °C. at 90° K. The average specific heat over this temperature range is about 0.23 cal./g. °C. and the sensible heat is, therefore, 160 cal. per gram. This is about 105 times greater than the heat of adsorption. 

Two 800-kg cars moving at a velocity of 90 km/h have a head-on collision on a road. Both cars come to a complete rest after the crash. Assuming all the kinetic energy of cars is converted to thermal energy, determine the average temperature rise of the remains of the cars immediately after Ihe crash. Take the average specific heat of the cars to be 0.45 kJ/kg °C. 

Chickens with an average mass of 2.2 kg and average specific heat of 3.54 kJ/kg °C are to be cooled by chilled water that enters a continuous-flow-type immersion chiller at 0.5 C. Chickens ate dropped into the chiller at a uniform temperature of I5°C at a rate of SOO chickens per hour and are cooled to an average temperature of 3°C before they are taken out. The chiller gains heal Croin the surroundings at a rate of 210 kl/mio. Determine (removal from tiie chicken, in k V, and (b) Ihc mass flow rate of water, in kg/s, if the temperature rise of water is not to exceed 2°C. 

In general, m is approximately zero in the high pressure region for most propellants. However, T of nitropolymer propellants such as single-base and double-base propellants decreases as pressure decreases below about 5 MPa. Since the direct determination of m is difficult, the heat of explosion Hexp is evaluated as a function of pressure. The flame temperature termed T is determined by assuming an average specific heat of the combustion products, cp, as... 

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