Adiabatic processes expansion/compression

A thermodynamic change of state of a system such that no heat or mass is transferred across the boundaries of the system. In an adiabatic process, expansion always results in cooling, and compression in warming, adiabatic warming... 

The modulus indicates that heat is absorbed (+), during die isodrermal expansion, but released (—) during die isothermal compression. In the adiabatic processes no heat is supplied or removed from die working gas, and so... 

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 ... 

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 -... 

CARNOT CYCLE. An ideal cycle or four reversible changes in the physical condition of a substance, useful in thermodynamic theory. Starting with specified values of die variable temperature, specific volume, and pressure, the substance undergoes, in succession, an isothermal (constant temperature) expansion, an adiabatic expansion (see also Adiabatic Process), and an isothermal compression to such a point that a further adiabatic compression will return the substance to its original condition. These changes are represented on the volume-pressure diagram respectively by ub. he. ctl. and da in Fig. I. Or the cycle may he reversed ad c h a. 

The temperature [K] and pressure [atm] of the input and output streams are specified following the mark . The adiabatic nature of this process is disclosed by the value of AH. The exergy destruction ToEASi is, therefore, given by changing sign of the exergy increase of this adiabatic process. Adiabatic compression and expansion are other examples of the singular system. 

Consider now an irreversible process in a closed system wherein no heat transfer occurs. Such a process is represented on the P V diagram of Fig. 5.6, which shows an irreversible, adiabatic expansion of 1 mol of fluid from an initial equilibrium state at point A to a final equilibrium state at pointB. Now suppose the fluid is restored to its initial state by a reversible process consisting of two steps first, the reversible, adiabatic (constant-entropy) compression of tile fluid to tile initial pressure, and second, a reversible, constant-pressure step that restores tile initial volume. If tlie initial process results in an entropy change of tlie fluid, tlien tliere must be heat transfer during tlie reversible, constant-P second step such tliat ... 

Because no thermal insulation is perfect, truly adiabatic processes do not occur. However, heat flow does take time, so a compression or expansion that occurs more rapidly than thermal equilibration can be considred adiabatic for practical purposes. 

Now we repeat the experiment using a different adiabatic process B. The system is still closed, and the initial and final states are still [T, V ] and [T , V ], but we use a sequence of steps with various weights, so the volume changes in a different way hence, the degree of irreversibility differs from that in process A. In general, to achieve the required final state [T , y ] we may have to use some combination of compressions and expansions. The work required for this second process is... 

Adiabatic process Thermodynamic process in which there is no exchange of heat or mass between a metaphorical parcel of air and its surroundings thus, responding to the decrease in atmospheric density with height, rising air cools adiabatically due to expansion and sinking air warms due to compression. 

Equation (2.4-21) can be used for a reversible adiabatic compression as well as for an expansion. It is an example of an important fact that holds for any system, not just an ideal gas For a reversible adiabatic process in a simple system the final temperature is a function of the final volume for a given initial state. All of the possible final state points for reversible adiabatic processes starting at a given initial state lie on a single curve in the state space, called a reversible adiabat. This fact will be important in our discussion of the second law of thermodynamics in Chapter 3. 

The Carnot engine operates on a two-stroke cycle that is called the Carnot cycle. We begin the cycle with the piston at top dead center and with the hot reservoir in contact with the cylinder. We break the expansion stroke into two steps. The first step is an isothermal reversible expansion of the system at the temperature of the hot reservoir. The final volume of the first step is chosen so that the second step, which is an adiabatic reversible expansion, ends with the system at the temperature of the cold reservoir and with the piston at bottom dead center. The compression stroke is also broken into two steps. The third step of the cyclic process is a reversible isothermal compression with... 

To help solidify these abstract ideas, a concrete example is illustrative. We will compare the value of work for six processes. We will label these cases process A through process F. Three processes (A, C, and E) entail isothermal expansion of a piston-cylinder assembly between the same states state 1 and state 2. The other three (B, D, and F) consist of the opposite process, isothermal compression between state 2 and state 1. An isothermal process results in the limit of fast heat transfer with the surroundings. We could perform a similar analysis on adiabatic processes where there is no energy transfer via heat between the system and the surroundings. 

To illustrate how entropy tells us about the directionahty of nature, we first pick a set of four mechanical processes similar to those described in Figure 3.2a (1) reversible expansion, (2) irreversible expansion, (3) reversible compression, and (4) irreversible compression. In this case, however, we choose adiabatic rather than isothermal processes. The adiabatic process represents the limit of no heat transfer between the system and the... 

Again, for a reversible, adiabatic process the entropy of the system remains constant. Likewise, the entropy changes of the surroundings and universe are zero. We see that the results for reversible, adiabatic compression are identical to the results presented in Table 3.1 for reversible, adiabatic expansion. An energy balance gives ... 

For an adiabatic reversible process (whether compression or expansion), the entropy of the system remains unchanged while for an irreversible process (whether compression or expansion), the entropy of the system increases. In both cases, the entropy changes for the surroundings are zero. Therefore, the entropy change of the universe remains unchanged for a reversible process and increases for an irreversible process. 

The thermal efficiency of the process (QE) should be compared with a thermodynamically ideal Carnot cycle, which can be done by comparing the respective indicator diagrams. These show the variation of temperamre, volume and pressure in the combustion chamber during the operating cycle. In the Carnot cycle one mole of gas is subjected to alternate isothermal and adiabatic compression or expansion at two temperatures. By die first law of thermodynamics the isothermal work done on (compression) or by the gas (expansion) is accompanied by the absorption or evolution of heat (Figure 2.2). 

It follows that the efficiency of the Carnot engine is entirely determined by the temperatures of the two isothermal processes. The Otto cycle, being a real process, does not have ideal isothermal or adiabatic expansion and contraction of the gas phase due to the finite thermal losses of the combustion chamber and resistance to the movement of the piston, and because the product gases are not at tlrermodynamic equilibrium. Furthermore the heat of combustion is mainly evolved during a short time, after the gas has been compressed by the piston. This gives rise to an additional increase in temperature which is not accompanied by a large change in volume due to the constraint applied by tire piston. The efficiency, QE, expressed as a function of the compression ratio (r) can only be assumed therefore to be an approximation to the ideal gas Carnot cycle. 

Figure 3.4 Carnot cycle for the expansion and compression of an ideal gas. Isotherms alternate with adiabats in a reversible closed path. The shaded area enclosed by the curves gives the net work in the cyclic process.

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