Chapter 6: Entropy First law: Energy conservation concept. Introduction of the concept of internal energy, u, to use the first law quantitatively for a process. Second law: Indicates that natural processes proceed in a certain direction but not in the opposite direction – qualitative in nature The difference between an ideal engine (such as the Carnot engine) and a real engine is that the ideal engine involves reversible processes, but a real engine involves real processes that are irreversible. Ideal reversible processes in an ideal engine may lead to a maximum engine efficiency A real process will deviate from the reversible process. Then, how much?
Inequality of Clausius Entropy S: A parameter introduced to describe the deviation of a real process from the corresponding ideal reversible process, or to measure the irreversibility A parameter to treat the second law quantitatively Inequality of Clausius (6.1) It can be demonstrated that it is valid for all possible cycles, including both reversible and irreversible heat engines and refrigerators.
Inequality of Clausius For a reversible engine (Carnot engine):
Entropy generation
Defining Entropy as a Property of a System Consider cycle 1-A-2-B-1 (all cycles here are reversible cycles!) All the processes are reversible here except process d.
Defining Entropy as a Property of a System The change of the entropy following a reversible and an irreversible process (such as process d) between the same initial and final states is identical.
Retrieving Entropy Data/The entropy of a pure substance
Using the T-ds Equations
Entropy change of an ideal gas Specific heats are not constant. Use of ideal gas tables such as A-22 is more accurate.
Entropy change of a solid or liquid
Entropy change in Internally Reversible Processes
Entropy Balance for Closed Systems
Entropy production/Increase of entropy principle Or entropy production Or entropy production Entropy is NOT conserved. It may be increased due to the heat transfer into the system or generated because of irreversibility, but it may also be reduced due to the heat transfer out of the system,
Entropy Rate Balance for Control Volume
Isentropic process for an ideal gas Differentiating on both sides of the ideal gas law
Isentropic process for an ideal gas The relation is cited here for comparison with the CV related relation to be introduced later. The above derivation as did in Chapter 2 did not involve entropy concept.
Isentropic Efficiencies of Turbines, Nozzles, Compressors, and Pumps The isentropic efficiencies involve a comparison between the actual performance of a device and the performance that would be achieved under idealized circumstances for the same inlet state and the same exit pressure. In the following analyses, the effects of heat transfer, kinetic energy, and potential energy are ignored. With the condition of an isentropic process, the state at 2s can be easily determined.
Isentropic Efficiencies of Nozzles
Isentropic Efficiencies of Compressors and Pumps
Heat transfer/work in internally reversible, steady-state flow processes The work relation of an open system differs from the closed system because of the flow work is included in the inlet and outlet energies in terms of enthalpies h1 and h2. For an adiabatic process, the same relation may be obtained by noticing that: Expansion, dp<0, W > 0, turbines Compression, dp>0, W<0, compressors
Work in Polytropic Processes
Work in Polytropic Processes with Ideal Gases
Work in Polytropic Processes
DO NOT confuse with the relations for control mass or system below:
Polytropic Processes
Polytropic process/Isentropic process A polytropic process is a quasi-equilibrium process, which consists of a series of equilibrium states. A polytropic process may be considered as an internally reversible process (p. 246, 7 ed.) If these is no heat transfer through the polytropic process, the process is an isentropic process. In this case, n = k.
Key equations
Key equations The relative pressure and relative volume are all a function of temperature only.