Pressure reversible/irreversible processes

Essentially this requirement means that, during die irreversible process, innnediately inside die boundary, i.e. on the system side, the pressure and/or the temperature are only infinitesimally different from that outside, although substantial pressure or temperature gradients may be found outside the vicinity of the boundary. Thus an infinitesimal change in p or T would instantly reverse the direction of the energy flow, i.e. the... 

We shall suppose the solute to be a mol of an ideal gas, occupying a volume v at the pressure o and the solvent a volume Y of Iig. 56. liquid just sufficient to dissolve all the gas under the pressure j)o- If the gas is brought directly into contact with the liquid, an irreversible process of solution occurs, but if it is first of all expanded to a very large volume, the dissolution may be made reversible, except for the first trace of gas entering the... 

Besides the reversible and irreversible processes, there are other processes. Changes implemented at constant pressure are called isobaric process, while those occurring at constant temperature are known as isothermal processes. When a process is carried out under such conditions that heat can neither leave the system nor enter it, one has what is called an adiabatic process. A vacuum flask provides an excellent example a practical adiabatic wall. When a system, after going through a number of changes, reverts to its initial state, it is said to have passed through a cyclic process. 

For an irreversible adiabatic expansion in which some work is performed, the work performed is less in magnimde than that in the reversible process because the external pressure is less than the pressure of the gas by a finite amount. Thus, if the final volume is the same as in the reversible process, the final temperature will not be as low in the irreversible process, because, according to Equation (5.47), the temperature drop depends directly on the work performed by the expanding gas. Similarly, from Equations (5.42) and (5.44), AC7 and A//, respectively, also must be numerically smaller in the intermediate expansion than in the reversible expansion. In the adiabatic expansion, from a common set of initial conditions to the same final volume, the values of Af7 and A//, as well as the values of the work performed, seem to depend on the path (see summary in Table 5.2). At first glance, such behavior seems to contradict the assumption that U and H are state functions. Careful consideration shows that the difference occurs because the endpoints of the three paths are different. Even though the final volume can be made the same, the final temperature depends on whether the expansion is free, reversible, or intermediate (Table 5.2). 

We conclude by summarizing in Table 3.1 some key distinctions between reversible and irreversible processes, taking as an example the expansion of a gas against a piston, with external pressure Fext ... 

The orifice coefficient K takes into account both frictional pressure losses, and conversion of pressure to velocity. The frictional losses represent an irreversible process. The conversion of pressure to velocity represent a reversible process. 

Expansion against an external pressure that differs by a finite (measurable) amount is an irreversible process in the sense that an infinitesimal change in the external pressure does not reverse the direction of travel of the piston. For instance, if the pressure of the system is 2.0 atm... 

Equation (12-2) leads to the following criterion for spontaneity for a process occurring at constant temperature and pressure, but with the system in thermal and mechanical contact with the surroundings The Gibbs free energy decreases for a spontaneous (irreversible) process and remains constant for an equilibrium (reversible) process. 

Consider a simple system where the only work is a volume expansion against an external pressure (Fig. 2.2). In this case, for either a reversible or irreversible process, it can be shown that... 

The maximum work the system can do occurs when dP -> 0. Wi ax " P0 y When the system does the maximum work, in other words, the system undergoes a reversible process, then from the first law of thermodynamics AU = q - w = qr - wmax or qr = AU + wmax q, is the maximum amount of heat which the system can absorb from the surroundings (heat reservoir) for the vaporisation of 1 mole of water. If the pressure drop, dP, is a finite amount, i.e., dP 0, in other words, the system undergoes an irreversible process, then the system does less work for the same volume expansion w = (Po-dP)P < hw Heat transferred from the surroundings to the system is q = AU + w... 

If one suddenly opens the tap (valve) on a cylinder containing a gas confined under a pressure Pi (much greater than atmospheric pressure, Patm (i.e. P, 3> Patm)) and allows it to escape by into the atmosphere this process will continue until the pressures are equalised and the final pressure Pf = Patm. The expansion (leaving aside all discussion of throttle effects at the valve, gas/air mixing, friction effects etc.) takes place rapidly - and under non-equilibrium conditions - usually at constant temperature, T (= ambient) and is a spontaneous process. Since this process is not at equilibrium and hence is not reversible, we refer to it as being an irreversible process. 

Since the heat supplied, Aq at constant pressure, P is equal to the change in enthalpy, AH, which is itself a state function - and is therefore identical for both reversible and irreversible processes - hence we can write ... 

For a vstem at constant pressure and temperature, we see that the Gibbs free energy is constant for a reversible process but decreases for an irreversible process, reaching aminimum value consistent with the pressure and temperature for the equilibrium state just as for a system at constant volume the Helmholtz free energy is constant for a reversible process but decreases for an irreversible process. As with A, we can get the equation of state and specific heat from the derivatives of <7, in equilibrium. We have... 

The above examples demonstrate the DSR concept as a useful approach to generate and interrogate simultaneously complex systems for different applications. A range of reversible reactions, in particular carbon-carbon bond-formation transformations, was used to demonstrate dynamic system formation in both organic and aqueous solutions. By applying selection pressures, the optimal constituents were subsequently selected and amplified from the dynamic system by irreversible processes under kinetic control. The DSR technique can be used not only for identification purposes, but also for evaluation of the specificities of selection pressures in one-pot processes. The nature of the selection pressure applied leads to two fundamentally different classes external selection pressures, exemplified by enzyme-catalyzed resolution, and internal selection pressures, exemplified by transformation- and/or crystallization-induced resolution. Future endeavors in this area include, for example, the exploration of more complex dynamic systems, multiple resolution schemes, and variable systemic control. 

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 ... 

A single gas stream enters a process at conditions T, P, and leaves at pressure P2. The process is adiabatic. Prove that the outlet temperahire T2 for the actual (irreversible) adiabatic process is greater than that for a reversible adiabatic process. Assume the gas is ideal with constant heat capacities. 

The mere fact that a substantial change can be broken down into a very large number of small steps, with equilibrium (with respect to any applied constraints) at the end of each step, does not guarantee that the process is reversible. One can modify the gas expansion discussed above by restraining the piston, not by a pile of sand, but by the series of stops (pins that one can withdraw one-by-one) shown in figure A2.1.3. Each successive state is indeed an equilibrium one, but the pressures on opposite sides of the piston are not equal, and pushing the pins back in one-by-one will not drive the piston back down to its initial position. The two processes are, in fact, quite different even in the infinitesimal limit of their small steps in the first case work is done by the gas to raise the sand pile, while in the second case there is no such work. Both the processes may be called quasi-static but only the first is anywhere near reversible. (Some thermodynamics texts restrict the term quasi-static to a more restrictive meaning equivalent to reversible , but this then leaves no term for the slow irreversible process.)... 

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