Isentropic compression-expansion

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.

This result, called the Riemann Integral, can be applied to unsteady isentropic compression waves as well as to expansion waves. By defining a Riemann function ... 

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. 

In Example 14.3 and Problem 14.6 use has been made of entropy — enthalpy diagrams. The change in enthalpy due to isentropic compression or expansion may also be calculated, however, using equations 8.30 and 8.32 in Volume 1. 

Assume isentropic for compression process 1-2, isentropic for compression process 2-3, isochoric for heating process 3-4, isentropic for expansion process 4-5, and isochoric for cooling process 5-6. 

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. 

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. 

A closed system cannot perforin an isentropic process without performing work. Example (Fig. 3) A quantity of gas enclosed by an ideal, tfictionless, adiabatic piston in an adiabatic cylinder is maintained at a pressure p by a suitable ideal mechanism, so that Gl = pA (A being the area of piston). When the weight G is increased (or decreased) by an infinitesimal amount dG, the gas will undergo an isentropic compression (or expansion). In this case,... 

Eqs. (7.18) and (7.19) derived for isentropic compression apply equally well for isentropic expansion. They combine to give ... 

Irreversibilities in the compressor and turbine greatly reduce the thermal, efficiency of the power plant, because the net work is the difference between the work required by the compressor and the work produced by the turbine. The temperature of the air entering the compressor TA and the temperature of the air entering the turbine, the specified maximum for Tc, are the same as for the ideal cycle. However, the temperature after irreversible compression in the compressor Ts is higher than the temperature after isentropic compression T B, and the temperature after i never - ible expansion in the turbine TD is higher than the temperature after isentropic expansion T d. 

The vapor-compression cycle incorporating an expansion valve is shown in Fig. 9.1h, where line A- 1 represents the constant-enthalpy throttling process. Line 2 + 3, representing an actual compression process, slopes in the direction of increasing entropy, reflecting the irreversibility inherent in the process. The dashed line 2 - 3 is the path of isentropic compression (see Fig. 7.6). For this cycle, the coefficient of performance is simply... 

Helmholtz energy Gibbs energy Isobaric heat capacity Isochoric heat capacity Isobaric expansivity Isothermal compressibility Isentropic compressibility... 

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