Category: Entropy

4.1. Extending Example 4.2 on page 141 from solids to gases is straightforward if you recall the development of Eqn. 1.13 on page 19. Consider N2 for example. Being diatomic, we should expect that Uig = 2(3NAkT/2) = 6RT/2 in the limit of classical vibrations. Vibrational energy means that heat can be absorbed in the vibration of a bond.…

In this section, we refer to a division of the universe into the same three subsystems described in Section 2.14 on page 74. 1. T is the system temperature at the location where Q is transferred. 2. Sin, Sout are state variables, and any pathway may be used to calculate the change from inlet to outlet. The pathway for calculation does not need to be the pathway for…

We end the chapter by providing examples of unsteady-state open systems. The first example shows that analysis of such systems can produce results quite consistent with expansion in a piston/cylinder. Example 4.19. Entropy change in a leaky tank Consider air (an ideal gas) leaking from a tank. How does the entropy of the gas in…

A fascinating feature of living systems is that they organize small molecules into large structures. Towering pines grow with energy from the sun, CO2, water, and minerals extracted from the ground. Mammals grow into sophisticated thinking creatures by consuming small bits of food, consuming water, and breathing air. Small mindless flagella are known to swim…

Let us consider how to calculate the optimum work interactions for a general system. For an open system where kinetic energy and potential energy changes are negligible, where dSgen = 0 for an internally reversible process. If all the heat is transferred at a single temperature Tsys, elimination of dQ in the first balance provides If we wish to apply this…

When solving thermodynamic problems, usually the best approach is to begin by applying the mass and energy balances. The entropy balance provides another balance, but it is not always necessary for every problem. In this chapter, we have introduced some new terms which can specify additional constraints when used in the problem statement, e.g., “isentropic,” “reversible,” “internally…

An irreversible, adiabatic pump or compressor generates entropy. If these devices are reversible, they are isentropic. Examples of both are shown in Fig. 4.12. The calculations are generally straightforward. Consider the case where the inlet state and the outlet pressure is known. First, the reversible outlet state is determined based on the isentropic condition, and the…

For a reversible adiabatic turbine, the entropy balance in Section 4.6 shows that the outlet entropy must equal the inlet entropy. For an irreversible turbine, the outlet entropy must be greater than the inlet entropy. We may now visualize the state change on the diagrams sketched in Section 4.8. For example, on a T-S diagram, the performance of a turbine…

Turbines, compressors, and pumps occur so frequently that we need convenient tools to aid in process calculations. Visualization of the state change is possible by plotting entropy on charts. This technique also permits the charts to be used directly in the process calculations. One common representation is the T-S chart shown in Fig. 4.6. The phase envelope appears…

Our analysis of the Carnot devices supports statement 2 at the beginning of Section 4.3. We have seen that work is maximized/minimized when the entropy generation is zero. Analysis of other processes would verify this useful conclusion. Work is lost by processes which generate entropy. If a device is not internally reversible, work will be lost within the…