Isentropic expansion and

Wiedermatm (1986b) presents an alternative method for calculating work done by a fluid. The method uses the lambda model to describe isentropic expansion, and permits work to be expressed as a function of initial conditions and only one fluid parameter, lambda. Unfortunately, this parameter is known for very few fluids. 

Otto Cycle. The Otto cycle consists of isentropic compression, constant volume heat addition, isentropic expansion, and constant-volume heat rejection. 

Fig. 4-7. Carnot process or reversible cycle. Starting at point A, the cycle consists of an isentropic compression, an isothermal expansion, an isentropic expansion, and an isothermal compression. All steps are reversible. The open arrows symbolize the heat flow in a real technical process where there are temperature drops in the heat transfer to and from the process medium. The entropy flows from the heat source to the heat sink respectively, correspond to the hatched lines in that case.

Fig. 28. Rankine cycle for superheat, where ( ) represents adiabatic (isentropic) compression ( ), isobaric heating ( ), vaporization (x x x x), superheating turbine expansion and (-----), heat rejection. To convert kPa to psi, multiply by 0.145. To convert kj to kcal, divide by 4.184.

As stated earlier, turboexpanders are normally used in cryogenic processes to produce isentropic expansion to cool down the process gas. Two common applications are natural gas processing plants and chemical plants. In natural gas processing plants, turboexpanders are installed to liquify heavier hydrocarbon components and produce lean natural gas with specified dew point limits to meet required standards. 

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... 

The first term is due to the irreversible expansion from V, to Vj, and the second term to the isentropic expansion from Vj to Vj. Adamczyk does not actually say how p3 should be chosen. A reasonable choice for seems to be the initial-peak shock overpressure, as calculated from Eq. (6.3.22). The equation presented above can be compared to the results of Guirao et al. (1979). They numerically evaluated the work done by the expanding contact surface. When the difference between... 

The specific internal energy of the fluid in the expanded state U2 can be determined as follows If a thermodynamic graph is used, assume an isentropic expansion (entropy s is constant) to atmospheric pressure po- Therefore, follow the constant-entropy line from the initial state to Po- Read h- and V2 at this point, and calculate the specific internal energy U2-... 

Assuming isentropic expansion of the combustion gases through the nozzle and Pe = Ptt, the exhaust velocity can be determined from the equation... 

The calculation of entropy is required for compression and expansion calculations. Isentropic compression and expansion is often used as a reference for real compression and expansion processes. The calculation of entropy might also be required in order to calculate other derived thermodynamic properties. Like enthalpy, entropy can also be calculated from a departure function ... 

USA in 1872. Thermodynamically, the cooling version consists of an adiabatic (isentropic) compression followed by heat transfer to the surroundings, then adiabatic expansion and cooling. 

Four methods are used to estimate the energy of explosion for a pressurized gas Brode s equation, isentropic expansion, isothermal expansion, and thermodynamic availability. Brode s method21 is perhaps the simplest approach. It determines the energy required to raise the pressure of the gas at constant volume from atmospheric pressure to the final gas pressure in the vessel. The resulting expression is... 

With the nomenclature used in Volume 2, Example 14.3, H = 2765 kJ/kg and, assuming isentropic expansion to 3.5 kN/m2, from the entropy—enthalpy chart ... 

Perform an isentropic expansion. That is, as the pressure decreases from P0 to the backpressure Pb (usually ambient pressure Pa), select intermediate values of pressure Pi. At each P1 find the temperature that keeps S constant 7 i. Solve for the vapor fraction x, using the entropy balance between planes 0 and 1 ... 

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