Gases constant-pressure processes

To calculate the heat duty it must be remembered that the pressure drop through the choke is instantaneous. That is, no heat is absorbed or lost, but there is a temperature change. This is an adiabatic expansion of the gas w ith no change in enthalpy. Flow through the coils is a constant pressure process, except for the small amount of pressure drop due to friction. Thus, the change in enthalpy of the gas is equal to the heat absorbed. 

The key to this solution lies in the fact that the operation involved is an irreversible expansion. Taking Cv as constant between P i and T2, AU = — W = nCv(T2 — Pi) where n is the kmol of gas and T2 and Pi are the final and initial temperatures, then for a constant pressure process, the work done, assuming the ideal gas laws apply, is given by ... 

This equation is a mathematical statement that T/V is constant in any constant-pressure process and T/tt is constant in any constant-volume process. Macromolecules in very dilute aqueous concentration imitate gas... 

Because the internal energy of an ideal gas is a function of temperature only, both enthalpy and Cp also depend on temperature alone. This is evident from the definition H = U + PV, or H = U + RT for an ideal gas, and from Eq. (2.21). Therefore, just as A U = j CvdT for any process involving an ideal gas, so AH = J CP dT not only for constant-pressure processes but for all finite processes. 

Let us examine this for an ideal gas. Keep in mind we are looking at a constant-pressure process. 

For an ideal gas, PV = nRT, where n is the number of moles and R is the universal gas constant. Since we are looking at a constant pressure process with a constant amount of material ... 

This provides a convenient criterion to evaluate the effect of heat added to the vessel during transfer of the fluid. When the ratio of heat added to mass removed idq/dm) is equal to kpy/(p -py) the pressure will remain constant. When the ratio dq/dm is greater than this value the pressure will tend to increase (this is usually controlled by releasing the gas with a control valve when a constant pressure is desired). Values of dq/dm less than py/cp -Py) will cause the pressure to decrease to the limiting case shown in Figs. 1-5 where dq = 0. Since k, py and p are functions of pressure, (4) and (5) are only valid for a constant pressure process. 

Refer to the Integrative Example. What volume of the synthesis gas, measured at STP and burned in an open flame (constant-pressure process), is required to heat 40.0 gal of water from 15.2 to 65.0 °C (Igal = 3.785 L.)... 

Combustors All gas turbine combustors perform the same function They increase the temperature of the high-pressure gas at constant pressure. The gas turbine combustor uses veiy little of its air (10 percent) in the combustion process. The rest of the air is used for cooling and mixing. The air from the compressor must be diffused before it enters the combustor. The velocity leaving the compressor is about 400-500 ft/sec (130-164 m/sec), and the velocity in the combustor must be maintained at about 10-30 ft/sec (3-10 iTi/sec). Even at these low velocities, care must be taken to avoid the flame to be carried downstream. To ensure this, a baffle creates an eddy region that stabi-hzes the flame and produces continuous ignition. The loss of pressure in a combustor is a major problem, since it affecls both the fuel consumption and power output. Total pressure loss is in the range of 2-8 percent this loss is the same as the decrease in compressor efficiency. 

Turboexpander sensitivity to process gas inlet pressure. As previously mentioned, variable speed turboexpanders are more sensitive to changes in normal operating conditions. Tlie pattern of TTE degradation, however, is the same as for constant speed turboexpanders (Figure 7-13a). In other words, TTE is more sensitive to pressure drop than to pressure rise. For instance, a 20% drop in gas inlet pressure will reduce TTE to 90% of the design value, whereas a 20% increase in gas inlet pressure reduces TTE to 99% of the design value. 

In the gas turbine (Brayton cycle), the compression and expansion processes are adiabatic and isentropic processes. Thus, for an isentropic adiabatic process 7 = where Cp and c are the specific heats of the gas at constant pressure and volume respectively and can be written as ... 

When the space above the suspension is subjected to compressed gas or the space under the filter plate is under a vacuum, filtration proceeds under a constant pressure differential (the pressure in the receivers is constant). The rate of filtration decreases due to an increase in the cake thickness and, consequently, flow resistance. A similar filtration process results from a pressure difference due to the hydrostatic pressure of a suspension layer of constant thickness located over the filter medium. 

But another approach to multi-step cooling [8, 9] involves dealing with the turbine expansion in a manner similar to that of analysing a polytropic expansion. Fig. 4.4 shows gas flow (1 + ijj) at (p,T) entering an elementary process made up of a mixing process at constant pressure p, in which the specific temperature drops from temperature T to temperature T, followed by an isentropic expansion in which the pressure changes to (p dp) and the temperature changes from T to (7 - - dT). 

At the instant a pressure vessel ruptures, pressure at the contact surface is given by Eq. (6.3.22). The further development of pressure at the contact surface can only be evaluated numerically. However, the actual p-V process can be adequately approximated by the dashed curve in Figure 6.12. In this process, the constant-pressure segment represents irreversible expansion against an equilibrium counterpressure P3 until the gas reaches a volume V3. This is followed by an isentropic expansion to the end-state pressure Pq. For this process, the point (p, V3) is not on the isentrope which emanates from point (p, V,), since the first phase of the expansion process is irreversible. Adamczyk calculates point (p, V3) from the conservation of energy law and finds... 

Adiabatic Reaction Temperature (T ). The concept of adiabatic or theoretical reaction temperature (T j) plays an important role in the design of chemical reactors, gas furnaces, and other process equipment to handle highly exothermic reactions such as combustion. T is defined as the final temperature attained by the reaction mixture at the completion of a chemical reaction carried out under adiabatic conditions in a closed system at constant pressure. Theoretically, this is the maximum temperature achieved by the products when stoichiometric quantities of reactants are completely converted into products in an adiabatic reactor. In general, T is a function of the initial temperature (T) of the reactants and their relative amounts as well as the presence of any nonreactive (inert) materials. T is also dependent on the extent of completion of the reaction. In actual experiments, it is very unlikely that the theoretical maximum values of T can be realized, but the calculated results do provide an idealized basis for comparison of the thermal effects resulting from exothermic reactions. Lower feed temperatures (T), presence of inerts and excess reactants, and incomplete conversion tend to reduce the value of T. The term theoretical or adiabatic flame temperature (T,, ) is preferred over T in dealing exclusively with the combustion of fuels. 

Figure 15.5 shows the ideal open cycle for the gas turbine that is based on the Brayton Cycle. By assuming that the chemical energy released on combustion is equivalent to a transfer of heat at constant pressure to a working fluid of constant specific heat, this simplified approach allows the actual process to be compared with the ideal, and is represented in Figure 15.5 by a broken line. The processes for compression 1-2 and expansion 3-4 are irreversible adiabatic and differ, as shown from the ideal isentropic processes between the same pressures P and P2 -... 

The work done by any system on its surroundings during expansion against a constant pressure is calculated from Eq. 3 for a reversible, isothermal expansion of an ideal gas, the work is calculated from Eq. 4. A reversible process is a process that can be reversed by an infinitesimal change in a variable. 

Self-Test 6.6B Suppose that 1.00 kj of energy is transferred as heat to oxygen in a cylinder fitted with a piston the external pressure is 2.00 atm. The oxygen expands from 1.00 L to 3.00 L against this constant pressure. Calculate w and AU for the entire process by treating the 02 as an ideal gas. 

Apparatus. Since all the polymer modification reactions presented in this paper involved gas consumption, an automated gas consumption measuring system was designed, fabricated and used to keep constant pressure and record continuously the consumption of gas in a batch type laboratory scale reactor. Process control, data acquisition, and analysis was carried out using a personal computer (IBM) and an interface device (Lab-master, Tecmar Inc.). 

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