Summary

We are trying to be very careful throughout this chapter to anticipate every possibility that might arise. As a result, the verbiage gets very dense. Think of the complete energy balance as a checklist, reminding you to consider whether each term may contribute significantly to a given problem, and learning to translate key terms like “frictionless,” “reversible,” “continuous,” and “steady state” into meaningful reductions of the balance.

Important Equations

If we relax the formality, we can summarize most of this chapter casually as follows:

Naturally, it is best to appreciate how these equations result from simplifications. Remember to check the general energy balance for terms that may be significant in exceptional situations.

A summary of expansion/contraction work relations for ideal gases is also presented here, however it is recommended that you become proficient in the manipulations leading to these formulas. Section 2.4 summarizes factors that may make a process irreversible. The following formulas represent reversible work done when the system pressure is inserted for the isothermal process. The isobaric formula is the only one that can be used to directly calculate work done on the surroundings in an irreversible process, and in that case the surrounding pressure is used instead of the system pressure.

This last equation (for T₂/T₁) recurs frequently as we examine processes from various perspectives and simplify them to ideal gases for preliminary consideration. You should commit it to memory soon and learn to recognize when it is applicable.

Test Yourself

1. Write the energy balance without looking at the book. To help remember the terms, think about the properties the terms represent rather than memorizing the symbols.

2. In the presentation of the text, which side of the balance represents the system and which terms represent interactions at the boundaries?

3. Explain the terms “closed-system,” “open-system,” and “steady state” to a friend of the family member who is not an engineer.

4. Explain how a reference state helps to solve problems. Select a reference state for water that is different from the steam table reference state. Create a path starting from saturated liquid below the normal boiling point, through the normal boiling point, and cooling down to saturated vapor at the initial temperature. Use heat capacities and the latent heat at the normal boiling point to estimate the heat of vaporization and compare it with the steam table value.

5. Write a MATLAB, Excel, or calculator routine that will enable you to calculate heat capacity integrals easily.

6. Think of as many types of paths as you can from memory (isothermal, adiabatic, etc.) and try to derive the heat and work flow for a piston/cylinder system along each path.