Isentropic process processes

Now the system is thennally insulated and the magnetic field is decreased to zero in this adiabatic, essentially reversible (isentropic) process, the temperature necessarily decreases since... 

The fact that shock waves continue to steepen until dissipative mechanisms take over means that entropy is generated by the conversion of mechanical energy to heat, so the process is irreversible. By contrast, in a fluid, rarefactions do not usually involve significant energy dissipation, so they can be regarded as reversible, or isentropic, processes. There are circumstances, however, such as in materials with elastic-plastic response, in which plastic deformation during the release process dissipates energy in an irreversible fashion, and the expansion wave is therefore not isentropic. 

The Brayton cycle in its ideal form consists of two isobaric processes and two isentropic processes. The two isobaric processes consist of the combustor system of the gas turbine and the gas side of the HRSG. The two isentropic processes represent the compression (Compressor) and the expansion (Turbine Expander) processes in the gas turbine. Figure 2-1 shows the Ideal Brayton Cycle. 

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 ... 

TNT explosions have a very high shock pressure close to the blast source. Because a shock wave is a non-isentropic process, energy is dissipated as the wave travels from the source, thus causing rapid decay of overpressures present at close range. 

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 -... 

For an isentropic process the enthalpy may be expressed as a function of the pressure and... 

The velocity uw = fkP2v2 is shown to be the velocity of a small pressure wave if the pressure-volume relation is given by Pifi = constant. If the expansion approximates to a reversible adiabatic (isentropic) process k y, the ratio of the specific heats of the gases, as indicated in equation 2.30. 

A general ideal gas adiabatic (isentropic) compression process is given by ... 

Water decompression may be assumed to be an isentropic equilibrium process for unheated blowdown or limited heating of fluid in the core region in order to calculate the transient pressure-time relationships with reasonably good accuracy for the full duration of the blowdown. 

However, for a rarefaction wave, the vapor becomes subcooled and the liquid becomes superheated. When the wave front passes, the liquid phase is assumed to adjust from the metastable state at an equilibrium rate. If isentropic processes are assumed, the mass transfer rate can be shown to be... 

If we compare the work required to compress a given gas to a given compression ratio by isothermal and isentropic processes, we see that the isothermal work is always less than the isentropic work. That is, less energy would be required if compressors could be made to operate under isothermal conditions. However, in most cases a compressor operates under more nearly adiabatic conditions (isentropic, if frictionless) because of the relatively short residence time of the gas in the compressor, which allows very little time for heat generated by compression to be transferred away. The temperature rise during an isentropic compression is determined by eliminating p from Eqs. (8-17) and (8-19) ... 

During process 1-2, the system is thermally insulated and the temperature of the working substance is raised from the low temperature Tl to the high temperature T-. The process is an isentropic process. The amount of heat transfer during the process is = J TAS = d, because there is no area underneath a constant entropy (vertical) line. 

COMMENTS The Carnot vapor cycle as illustrated by Example 2.1 is not practical. Difficulties arise in the isentropic processes of the cycle. One difficulty is that the isentropic turbine will have to handle steam of low quality. The impingement of liquid droplets on the turbine blade causes erosion and wear. Another difficulty is the isentropic compression of a liquid-vapor mixture. The two-phase mixture of the steam causes serious cavitation problems during the compression process. Also, since the specific volume of the saturated mixture is high, the pump power required is also very high. Thus, the Carnot vapor cycle is not a realistic model for vapor power cycles. 

Water enters the pump at state 1 as a low-pressure saturated liquid to avoid the cavitation problem and exits at state 2 as a high-pressure compressed liquid. The heat supplied in the boiler raises the water from the compressed liquid at state 2 to saturated liquid to saturated vapor and to a much higher temperature superheated vapor at state 3. The superheated vapor at state 3 enters the turbine where it expands to state 4. The superheating moves the isentropic expansion process to the right on the T-s diagram as shown in Fig. 2.5, thus preventing a high moisture content of the steam as it exits the turbine at state 4 as a saturated mixture. The exhaust steam from the turbine enters the condenser at state 4 and is condensed at constant pressure to state 1 as saturated liquid. 

The thermodynamic power cycles most commonly used today are the vapor Rankine cycle and the gas Brayton cycle (see Chapter 4). Both are characterized by two isobaric and two isentropic processes. The vapor... 

The Carnot cycle is not a practical model for vapor power cycles because of cavitation and corrosion problems. The modified Carnot model for vapor power cycles is the basic Rankine cycle, which consists of two isobaric and two isentropic processes. The basic elements of the basic Rankine cycle are pump, boiler, turbine, and condenser. The Rankine cycle is the most popular heat engine to produce commercial power. The thermal cycle efficiency of the basic Rankine cycle can be improved by adding a superheater, regenerating, and reheater, among other means. 

An engine operates on an Otto cycle with a compression ratio of 8. At the beginning of the isentropic compression process, the volume, pressure, and temperature of the air are 0.01 m, llOkPa, and 50°C. At the end of the combustion process, the temperature is 900°C. Find (a) the temperature at the remaining two states of the Otto cycle, (b) the pressure of the gas at the end of the combustion process, (c) the heat added per unit mass to the engine in the combustion chamber, (d) the heat removed per unit mass from the engine to the environment, (e) the compression work per unit mass added, (f) the expansion work per unit mass done, (g) MEP, and (h) thermal cycle efficiency. 

An ideal Diesel cycle with a compression ratio of 17 and a cut-off ratio of 2 has an air temperature of 105°F and a pressure of ISpsia at the beginning of the isentropic compression process. Determine... 

An ideal Diesel cycle with a compression ratio of 17 and a cutoff ratio of 2 has a temperature of 313 K and a pressure of 100 kPa at the beginning of the isentropic compression process. Use the cold air-standard assumptions and assume that k= A. Determine (a) the temperature and pressure of the air at the end of the isentropic compression process and at the end of the combustion process, and (b) the thermal efficiency of the cycle. 

The isochoric heating process of a Lenoir engine receives air at 15°C and 101 kPa. The air is heated to 2000° C, and the mass of air contained in the cylinder is 0.01kg. Determine the pressure at the end of the isochoric heating process, the temperature at the end of the isentropic expansion process, heat added, heat removed, work added, work... 

A proposed air standard piston ylinder arrangement cycle consists of an isentropic compression process, a constant-volume heat addition process, an isentropic expansion process, and a constant-pressure heat-rejection process. The compression ratio (V1/V2) during the isentropic compression process is 8.5. At the beginning of the compression process, P=100kPa and r=300 K. The constant-volume specific heat addition is 1400kJ/kg. Assume constant specific heats at 25°C. 

The Otto cycle is a spark-ignition reciprocating engine consisting of an isentropic compression process, a constant-volume combustion process, an isentropic expansion process, and a constant-volume cooling process. The thermal efficiency of the Otto cycle depends on its compression ratio. The compression ratio is defined as r= Fmax/f min- The Otto cycle efficiency is limited by the compression ratio because of the engine knock problem. 

The ideal Brayton gas turbine cycle (sometimes called Joule cycle) is named after an American engineer, George Brayton, who proposed the cycle in the 1870s. The gas turbine cycle consists of four processes an isentropic compression process 1-2, a constant-pressure combustion process 2-3, an isentropic expansion process 3-4, and a constant-pressure cooling process 4-1. The p-v and T-s diagrams for an ideal Brayton cycle are illustrated in Fig. 4.1. 

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