Before we start several more complicated example problems, it will be helpful to outline the strategies which will be applied. We provide these in a step form to make them easier to use. Many of these steps will seem obvious, but if you become stuck when working through a problem, it is usually because one of these steps was omitted or applied inconsistently with system boundaries.
1. Choose system boundaries; decide whether this boundary location will make the system open or closed.
2. Identify all given state properties of fluids in system and crossing boundaries. Identify which are invariant with time. Identify your system as steady or unsteady state. (For unsteady-state pumps, turbines, or compressors, the accumulation of energy within the device is usually neglected.) For open, steady-state systems, write the mass balance and solve if possible.
3. Identify how many state variables are unknown for the system. Recall that only two state variables are required to specify the state of a pure, single-phase fluid. The number of unknowns will equal the number of independent equations necessary for a solution. (Remember in a system of known total volume V, that if n is known, the state variable V is known.)
The phase rule is important in determining the required number of equations.
4. Write the mass balance and the energy balance. These are the first equations to be used in the solution. Specify reference states for all fluids if necessary. Simplify energy balance to eliminate terms which are zero for the system specified in step 1.15 Combine the mass balance and the energy balance for open systems.
For unsteady-state problems:
a. Identify whether the individual terms in the energy balance may be integrated directly without combining with other energy balance terms. Often the answer is obtained most easily this way. This is almost always possible for closed-system problems.
b. If term-by-term integration of the energy balance is not possible, rearrange the equation to simplify as much as possible before integration.
Always consider the overall balance.
5. Look for any other information in the problem statement that will provide additional equations if unknowns remain. Look for key words such as adiabatic, isolated, throttling, nozzle, reversible, and irreversible. Using any applicable constraints of throttling devices, nozzles, and so on, relate stream properties for various streams to one another and to the system state properties. Constraints on flow rates, heat flow, and so on. provide additional equations. With practice, many of these constraints may be recognized immediately before writing the energy balance in steps 3 and 4.
6. Introduce the thermodynamic properties of the fluid (the equation of state). This provides all equations relating P, V, T, U, H, CP, and CV. The information will consist of either 1) the ideal gas approximation; 2) a thermodynamic chart or table; or 3) a volumetric equation of state (which will be introduced in Chapter 7). Using more than one of these sources of information in the same problem may introduce inconsistencies in the properties used in the solution, depending on the accuracy of the methods used.
Combine the thermodynamic information with the energy balance. Work to minimize the number of state variables which remain unknown. Many problems are solved at this point.
Use the same property method throughout the problem if possible.
7. Do not hesitate to move your system boundary and try again if you are stuck. Do not forget to try an overall balance (frequently, two open systems can be combined to give an overall closed system, and strategy 4a can be applied). Make reasonable assumptions.
Try different system boundaries.
8. After an answer is obtained, verify assumptions that were made to obtain the solution.
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