Isentropic change

These derivatives are also of interest for free expansions or isentropic changes. 

Corollary. In all reversible adiabatic changes the entropy remains constant such changes are therefore isentropic changes. 

Isentropic change. 75 lsochore, 44, 337 Isolated system, 37 Isomorphous mixture, 417 Isopiestic change, 44, 337 Isopneuma, 442 Isosteres, 442... 

In a reversible adiabatic change the entropy remains constant and therefore this type of change is called an isentropic change. Although not rigorously valid for irreversible changes, equations 6.32 to 6.34 are good approximations for these conditions. 

Putting k = y gives an approximate equation for adiabatic flow. The result is only approximate because it implies an isentropic change, ie a reversible adiabatic change, but this is not the case owing to friction. A rigorous solution for adiabatic flow is given in Section 6.5. 

When a system involves dissipative effects such as friction caused by molecular collisions or turbulence caused by a non-uniform molecular distribution, even under adiabahc conditions, ds becomes a positive value, and then Eqs. (1.13) and (1.14) are no longer valid. However, when these physical effects are very small and heat loss from the system or heat gain by the system are also small, the system is considered to undergo an isentropic change. 

The logarithmic form of Eq. (1.14) gives the specific heat raho under isentropic change as... 

Nozzleless rockets are very simplified and low-cost rockets because no nozzles are used. Their specific impulse is lower than that of conventional rockets even when the same mass of propellant is used. Normally, a convergent-divergent nozzle is used to expand the chamber pressure to the atmospheric pressure through an isentropic change, which is the most effective process for converting pressure into propulsive thrust The flow process without a nozzle increases entropy and there is stagnahon pressure loss. 

In the expansion wave, the flow velocity is increased and the pressure, density, and temperature are decreased along the stream line through the expansion fan. Since Oj > 02, it follows that Mi flow through an expansion wave is continuous and is accompanied by an isentropic change known as a Prandtl-Meyer expansion wave. The relationship between the deflection angle and the Mach number is represented by the Prandtl-Meyer expansion equation.l - l... 

Figure D-3. Pressure recovery with isentropic and non-isentropic changes.

If the flow process is an isentropic change, the total pressure poa remains unchanged throughout the nozzle flow. However, the process of the generation of a shock wave in the divergent part increases the entropy and the total pressure becomes Pq2- It is evident that the inlet performance increases as po2 approaches Po. ... 

Fig. 4.1-1. Isentropic change of state (CO2) AB, Gases CD, Liquids EF, Supercritical fluids.

Although Equation (4.1) is useful, particularly for isentropic changes of state for which dS = 0, the entropy appears as an independent variable. This circumstance is inconvenient from an experimental point of view, because no meters or devices exist that measure entropy. A new function in which the temperature is an independent variable rather than the entropy is obtained by subtracting... 

This chapter addresses the various phenomena indicated. In addition, the thermodynamic laws governing physical properties of the gas-solid mixture such as density, pressure, internal energy, and specific heat are introduced. The thermodynamic analysis of gas-solid systems requires revisions or modifications of the thermodynamic laws for a pure gas system. In this chapter, the equation of state of the gas-solid mixture is derived and an isentropic change of state is discussed. 

Another approach for estimating am is based on the pseudothermodynamic properties of the mixture, as suggested by Rudinger (1980). The equation for the isentropic changes of state of a gas-solid mixture is given by Eq. (6.53). Note that for a closed system the material density of particles and the mass fraction of particles can be treated as constant. Hence, in terms of the case for a single-phase fluid, the speed of sound in a gas-solid mixture can be expressed as... 

When gas flows from a stagnation condition through a nozzle under isentropic change, the enthalpy change is represented by Eq. (1.23). The flow velocity is obtained by the substitution of Eq. (1.14) into Eq. (1.24) as... 

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