Reversible adiabat

In the example of pressure-volume work in die previous section, the adiabatic reversible process consisted simply of the sufficiently slow motion of an adiabatic wall as a result of an infinitesimal pressure difference. The work done on the system during an infinitesimal reversible change in volume is then -pdVand one can write equation (A2.1.11) in the fomi... 

Figure A2.1.4. Adiabatic reversible (isentropic) paths that do not intersect. (The curves have been calculated for the isentropic expansion of a monatomic ideal gas.)...

There are now various adiabatic reversible paths because one can choose to vary dF or dF in any combination of steps. The paths can cross and intercoimect. The question of integrability is tied to the question... 

It suffices to carry out one such experiment, such as the expansion or compression of a gas, to establish that there are states inaccessible by adiabatic reversible paths, indeed even by any adiabatic irreversible path. For example, if one takes one mole of N2 gas in a volume of 24 litres at a pressure of 1.00 atm (i.e. at 25 °C), there is no combination of adiabatic reversible paths that can bring the system to a final state with the same volume and a different temperature. A higher temperature (on the ideal-gas scale Oj ) can be reached by an adiabatic irreversible path, e.g. by doing electrical work on the system, but a state with the same volume and a lower temperature Oj is inaccessible by any adiabatic path. 

State is adiabatic and reversible. Such an adiabatic reversible process is called an isentropic state change one in which the entropy remains constant. 

E3.13 A gas obeys the equation of state PVm RT + Bp and has a heat capacity Cy m that is independent of temperature. Derive an expression relating T and Vm in an adiabatic reversible expansion. 

Further insight can be gained from the idealized T - S diagram for the cycle. Figure 9-14. The compression of the air and fuel streams is represented here as a single adiabatic reversible (constant S) process in which the temperature of the gases rises above ambient. The heating of... 

For the reversible adiabatic expansion, we can see from Equation (5.42) that the final temperature T2 must be less than Ti, because W is negative and Cy is always positive. Thus, the adiabatic reversible expansion is accompanied by a temperature drop, and W, AU, and AH can be calculated from the measured initial and final temperatures using Equations (5.42) and (5.43). 

For a monatomic ideal gas, C i =3/2 R. Calculate the work performed in an adiabatic reversible expansion of 1 mole of this gas by integrating Equation (5.41). 

In any adiabatic reversible change, DQrev equals zero. Thus,... 

The first consists of two steps (1) an isothermal reversible expansion at the temperature Ta until the volume V is reached, and (2) an adiabatic reversible expansion from V to Vj,. The entropy change for the gas is given by the sum of the entropy changes for the two steps ... 

In Step II, a drop in temperature occurs in the adiabatic reversible expansion, but no change in entropy occurs. The isentropic nature of II is emphasized by the vertical line. Step III is an isothermal reversible compression, with a heat numerically equal to Qi being evolved. As this step is reversible and isothermal, we have from Equation (6.53)... 

The differential equations of fluid dynamics express conservation of mass, conse rvation of momentum, conservation of energy and an equation of state. For an adiabatic reversible process, viscosity and heat conduction processes are absent and the equations are 2.1.1 to 2.1.13, inclusive... 

We next carry out an adiabatic reversible expansion from B to C in which the additional quantity of work, W2, represented by the area BCV3V2 is done on the system (a negative value). During this expansion the cylinder is enclosed by an adiabatic envelope. No heat is transferred to the fluid, and its temperature decreases to 0X. 

We complete the proof by considering the adiabatic reversible expansion of an ideal gas. In this case we know that... 

We divide this equation by T and integrate between the limits T and T for the temperature and V and V for the volume, because the heat capacity of an ideal gas is a function of the temperature alone. Thus, for an adiabatic reversible expansion of an ideal gas... 

Equation (1.58) applies to any isothermal or adiabatic reversible cyclic processes. If there are many isothermal and adiabatic processes from high temperature TH to low temperature TL before the process goes back to its original state, any reversible cyclic process [Equation (1.58)] can be generalized as ... 

For the two adiabatic, reversible steps, we have PVy = const whence... 

The idealization of the gas-turbine cycle (based on air, and called the Bray cycle) is shown on a PV diagram in Fig. 8.12. The compression step AB represented by an adiabatic, reversible (isentropic) path in which the press increases from PA (atmospheric pressure) to PB. The combustion process replaced by the constant-pressure addition of an amount of heat QBC. Work produced in the turbine as the result of isentropic expansion of the air to press... 

Compressor efficiencies are usually expressed as isentropic efficiencies, i.e., on the basis of an adiabatic reversible process. Isothermal efficiencies are sometimes quoted, and design calculations are simplified when isothermal efficiencies are used. In either case, the efficiency is defined as the ratio of the power required for the ideal process to the power actually consumed. 

A certain gas obeys the equation of state P(V -nb) - nRT and has a constant volume heat capacity, Cv, which is independent of temperature. The parameter b is a constant. For 1 mol, find W, AE, Q, and AH for the following processes (a) Isothermal reversible expansion. (b) Isobaric reversible expansion. (c) Isochoric reversible process, (d) Adiabatic reversible expansion in terms of Tlf Vlt V2, Cp, and Cv subscripts of 1 and 2 denote initial and final states, respectively. (c) Adiabatic irreversible expansion against a constant external pressure P2, in terms of Plf P2, Tj, and 7 = (Cp/Cy). 

We now consider an adiabatically reversible process, since it is only under conditions of such isolation that one can hope to attain ultralow temperatures. On setting dS = 0, Eq. (1.18.1) becomes... 

The above expression carries an important general message any adiabatic reversible process resulting in a change of thermodynamic coordinates z necessarily alters the temperature of the system. 

When biomass is combusted under normal conditions, a flame is produced as visible radiation, provided oxidation occurs at a sufficient rate. By use of thermodynamic data, the theoretical temperature at which the products of combustion form under adiabatic, reversible conditions can be calculated. The theoretical flame temperature for the combustion of wood of various moisture... 

Fateh i M., Kaviany M. (1994) Adiabatic reverse combustion in a packed bed. Combustion and Flame, 99, 1-17. 

Entropy balance on gas contained in tank 1 initially and finally. This is a closed, adiabatic, reversible... 

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