Expansion, reversible work thermodynamics

A hypothetical cycle for achieving reversible work, typically consisting of a sequence of operations (1) isothermal expansion of an ideal gas at a temperature T2 (2) adiabatic expansion from T2 to Ti (3) isothermal compression at temperature Ti and (4) adiabatic compression from Ti to T2. This cycle represents the action of an ideal heat engine, one exhibiting maximum thermal efficiency. Inferences drawn from thermodynamic consideration of Carnot cycles have advanced our understanding about the thermodynamics of chemical systems. See Carnot s Theorem Efficiency Thermodynamics... 

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.)... 

The thermodynamic changes for reversible, free, and intermediate expansions are compared in the first column of Table 5.1. This table emphasizes the difference between an exact differential and an inexact differential. Thus, U and H, which are state functions whose differentials are exact, undergo the same change in each of the three different paths used for the transformation. They are thermodynamic properties. However, the work and heat quantities depend on the particular path chosen, even though the initial and final values of the temperature, pressure, and volume, respectively, are the same in all these cases. Thus, heat and work are not thermodynamic properties rather, they are energies in transfer between system and surroundings. 

Consequently, the energy of the gas is constant for the isothermal reversible expansion or compression and, according to the first law of thermodynamics, the work done on the gas must therefore be equal but opposite in sign to the heat absorbed by the gas from the surroundings. For a reversible process the pressure must be the pressure of the gas itself. Therefore, we have for the isothermal reversible expansion of n moles of an ideal gas between the volumes F and V... 

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 the process is reversible, and the work is restricted to work of expansion, as is almost invariably the case for processes considered in chemical thermodynamics, w may be replaced by PdV, where P is the pressure of the systmn, so that... 

Consider the special case of reversible processes on a single-component thermodynamic system. A differential element of work in expansion or compression is given by dw= — p dV, where p is the pressure and V is the volume. Using Eq. (10.55), the differential of heat equals dq = TdS. Therefore, the first faw (10.54) reduces to... 

All processes that are not reversible are called irreversible processes. The following examples can illustrate the nature of the irreversible process. Work W is done on a system the work is wholly or partly transformed into heat by friction within the system - the process cannot be reversed, it is irreversible. A gas expands into a vacuum during the expansion, pressure and temperature vary from one location to another inside the gas and thus, the gas is not in equilibrium during the expansion - the process cannot be reversed it is irreversible. A system at low temperature absorbs heat from surroundings with a high temperature during the heat exchange, the system is not in thermodynamic equilibrium - the process cannot be reversed it is irreversible. 

Rankine cycle An ideal reversible thermodynamic cycle used in steam power plants (see Fig. 49) that more closely approximates to the cycle of a real steam engine than the Carnot cycle and converts heat into mechanical work. It involves water being introduced under pressure into a boiler and evaporation taking place, followed by expansion of the vapour without the loss of heat, ending in condensation. The cycle therefore consists of four stages i) steam passes from the boiler to the cylinder at constant pressure ii) the steam expands adiabatically to the condenser pressure iii) heat is given to the condenser at constant temperature iv) condensation is completed and the condensate is remrned to the boiler. In the Rankine cycle, the work done is equivalent to the total heat in the steam at the end of the adiabatic expansion subtracted from the total heat in the steam at the beginning of the expansion. The heat supplied is equal to the sensible heat in the condensed steam subtracted from the total heat. 

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