Summary

This chapter started by introducing the concept of heat engines and heat pumps to interconverted heat and work, and the limitations in efficiency. As a cyclic process, the systems are simple, but practice builds confidence in working with multistep processes. In the distillation section we introduced quite a few terms because there are a lot of flow rates in the sections of a distillation column. This section provided practice in working with choice of boundaries for balances and working with many streams. Sorting out the streams that are relevant is a key step in the solution of problems. We introduced ideal gas mixtures and ideal solutions, stressing that the energy of mixing and volume of mixing are zero for both and so the enthalpy of a stream is the sum of the enthalpies of the constituents. We then used reference states to solve an energy balance on a mixed stream including a phase transition. In the section on reacting systems we set forth the procedures to properly account for energy flows in and out of the system. Finally we demonstrated that the energy balance was relevant for complex biochemical reactions. The energy balance for a reaction is independent of whether it occurs biologically or in an industrial reactor. The goal of this section was to demonstrate the breadth of applications and to build your confidence in solving problems. At this point most students still do not have a grasp on reversibility and irreversibility, which should be clarified in the next chapter as we build on this material.

Important Equations

Two equations that come up repeatedly are the Carnot efficiency (Eqn. 3.6) and Carnot COP (Eqn. 3.9). The Carnot efficiency teaches that the conversion of heat energy into mechanical energy cannot be 100% efficient, even if every operation in the process is 100% efficient. This has major implications throughout modern society, reflected in limitations on power plants and energy management. Much of Units I and II is devoted to understanding the details of these kinds of problems and how to solve them more precisely. The Carnot thermal efficiency and COP are benchmarks for real processes, though real processes are not always operating between reservoirs. Common errors applying the formulas are: (1) to interchange the formulas and use the COP formula when you want the efficiency; and (2) to use relative temperature (°C or °F) instead of absolute temperature.

This chapter introduced the concept of ideal solutions and methods of solving energy balances with mixtures, including phase transitions. Important equations are

We also introduced the concept of the reaction coordinate and that all species in a single reaction can be related by

We finished with the energy balance, which is most often expressed in the approximate form for the Heat of Reaction method:

If the enthalpy of formation is incorporated into the enthalpy of the components, the Heat of Formation method looks unchanged from the energy balance of Chapter 2: