- Entropy is a thermodynamic property that measures the degree of randomization or disorder at the microscopic level. The natural state of affairs is for entropy to be produced by all processes.
- A macroscopic feature which is associated with entropy production is a loss of ability to do useful work. Energy is degraded to a less useful form, and it is sometimes said that there is a decrease in the availability of energy.
- Entropy is an extensive thermodynamic property. In other words, the entropy of a complex system is the sum of the entropies of its parts.
- The notion that entropy can be produced, but never destroyed, is the second law of thermodynamics
Reversible and Irreversible Processes
Processes can be classed as reversible or irreversible. The concept of a reversible process is an important one which directly relates to our ability to recognize, evaluate, and reduce irreversibilities in practical engineering processes.
Consider an isolated system. The second law says that any process that would reduce the entropy of the isolated system is impossible. Suppose a process takes place within the isolated system in what we shall call the forward direction. If the change in state of the system is such that the entropy increases for the forward process, then for the backward process (that is, for the reverse change in state) the entropy would decrease. The backward process is therefore impossible, and we therefore say that the forward process is irreversible.
If a process occurs, however, in which the entropy is unchanged by the forward process, then it would also be unchanged by the reverse process. Such a process could go in either direction without contradicting the second law. Processes of this latter type are called reversible.
The key idea of a reversible process is that it does not produce any entropy.
Entropy is produced in irreversible processes. All real processes (with the possible exception of superconducting current flows) are in some measure irreversible, though many processes can be analyzed quite adequately by assuming that they are reversible. Some processes that are clearly irreversible include: mixing of two gases, spontaneous combustion, friction, and the transfer of energy as heat from a body at high temperature to a body at low temperature.
Recognition of the irreversibilities in a real process is especially important in engineering. Irreversibility, or departure from the ideal condition of reversibility, reflects an increase in the amount of disorganized energy at the expense of organized energy. The organized energy (such as that of a raised weight) is easily put to practical use; disorganized energy (such as the random motions of the molecules in a gas) requires “straightening out” before it can be used effectively. Further, since we are always somewhat uncertain about the microscopic state, this straightening can never be perfect. Consequently the engineer is constantly striving to reduce irreversibilities in systems, in order to obtain better performance.
Processes that are usually idealized as reversible include:
- Frictionless movement
- Restrained compression or expansion
- Energy transfer as heat due to infinitesimal temperature nonuniformity
- Electric current flow through a zero resistance
- Restrained chemical reaction
- Mixing of two samples of the same substance at the same state.
Processes that are irreversible include:
- Movement with friction
- Unrestrained expansion
- Energy transfer as heat due to large temperature non uniformities
- Electric current flow through a non zero resistance
- Spontaneous chemical reaction
- Mixing of matter of different composition or state.
Entropy Changes in an Ideal Gas
Many aerospace applications involve flow of gases (e.g., air) and we thus examine the entropy relations for ideal gas behavior. The starting point is form (a) of the combined first and second law,
We can think of Equation (5.2) as relating the fractional change in temperature to the fractional change of volume, with scale factors and ; if the volume increases without a proportionate decrease in temperature (as in the case of an adiabatic free expansion), then increases. Integrating Equation (5.2) between two states “1” and “2”:
For a perfect gas with constant specific heats
Equation 5.3 is in terms of specific quantities. For moles of gas,
This expression gives entropy change in terms of temperature and volume. We can develop an alternative form in terms of pressure and volume, which allows us to examine an assumption we have used. The ideal gas equation of state can be written as
Taking differentials of both sides yields
Using the above equation in Eq. (5.2), and making use of the relations ; , we find
Integrating between two states 1 and 2
Using both sides of (5.4) as exponents we obtain
Equation (5.5) describes a general process. For the specific situation in which , i.e., the entropy is constant, we recover the expression . It was stated that this expression applied to a reversible, adiabatic process. We now see, through use of the second law, a deeper meaning to the expression, and to the concept of a reversible adiabatic process, in that both are characteristics of a constant entropy, or isentropic, process.