Mean heat capacity

The use of mean heat capacities often facilitates the calculation of sensible-heat changes mean heat capacity over the temperature range r, to t2 is defined by the following equation  

Mean specific heat values are tabulated in various handbooks. If the values are for unit mass, calculated from some standard reference temperature, tr, then the change in enthalpy between temperatures i and t2 is given by  

Mean heat capacities for the combustion gases are readily available in handbooks and texts on heat and material balances. The following values are taken from K. A. Kobe, Thermochemistry of Petrochemicals, reprint No. 44, Pet. Ref. 1958 converted to SI units, J/mol°C, reference temperature 0°C. 

Heat extracted from the gas in cooling from 800 to 200° C, for each component  

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Heat Capacity. The mean heat capacity (0—900°C) at constant pressure, 6, in J/(kg- " C), can be estimated in vitreous silica using the following expression, where / is temperature in °C. 

Equations (4-140) and (4-141) may sometimes be advantageously expressed in alternative form through use of mean heat capacities ... 

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... 

Method 2. Use mean heat capacity data from Table 2-45 with reference conditions of P = 0 and T = 25°C for the combustion gases. Then the equation for T, becomes... 

A process requires a flow of 4 kg/s of purified water at 340 K to be heated from 320 K by 8 kg/s of untreated water which can be available at 380, 370, 360 or 350 K. Estimate the heat transfer surfaces of one shell pass, two tube pass heat exchangers suitable for these duties. In all cases, the mean heat capacity of the water streams is 4.18 kJ/kg K and the overall coefficient of heat transfer is 1.5 kW/m2 K. 

Component Molar mass (kg-krnol ) Mean heat capacity (kJkmoD K-1)... 

Alternatively, the heat capacity data can be used to derive mean heat capacities. The mean heat capacity can be defined as18 ... 

Table 15.15 presents mean heat capacity data between 25°C and a given temperature for a range of temperatures. 

This agrees well with the initial estimate. Had there been significant disagreement, then revised mean heat capacities would need to be taken and the calculation repeated, b. If 15% excess air is used, then combustion products are ... 

Again, estimate the theoretical flame temperature to be 2000°C. The mean heat capacities are as before and the heat balance is now ... 

What is the evaporation rate and yield of the sodium acetate hydrate CH3C00Na.3H20 from a continuous evaporative crystalliser operating at 1 kN/m2 when it is fed with 1 kg/s of a 50 per cent by mass aqueous solution of sodium acetate hydrate at 350 K The boiling point elevation of the solution is 10 degK and the heat of crystallisation is 150 kJ/kg. The mean heat capacity of the solution is 3.5 kJ/kg K and, at 1 kN/m2, water boils at 280 K at which temperature the latent heat of vaporisation is 2.482 MJ/kg. Over the range 270-305 K, the solubility of sodium acetate hydrate in water s at T(K) is given approximately by ... 

A solution containing 23 per cent by mass of sodium phosphate is cooled from 313 to 298 K in a Swenson-Walker crystalliser to form crystals of Na3P04.12H20. The solubility of Na3P04 at 298 K is 15.5 kg/100 kg water, and the required product rate of crystals is 0.063 kg/s. The mean heat capacity of the solution is 3.2 kJ/kg deg K and the heat of crystallisation is 146.5 kJ/kg. If cooling water enters and leaves at 288 and 293 K, respectively, and the overall coefficient of heat transfer is 140 W/m2 deg K, what length of crystalliser is required ... 

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 heat capacity of the solids is 2.2 kJ/kg deg K and 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 ... 

Given 10,000 Ib/hr of 700°F cycle exhaust gas passing through a heat recovery boiler (HRB) (a) How much 150 psia, 400°F steam can be produced (b) How much heat is transferred from the gas to the steam (c) What is the exhaust temperature of the gas leaving the HRB and (d) Sketch the T-Q (temperature-heat) diagram for the HRB. Assume a gas side mean heat capacity of 0.25 Btu/lb, °F, an evaporator pinch temperature of 30°F, a feedwater temperature of 60°F, and an evaporator drum pressure of 180 psia to allow for pressure losses. 

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