Modern Engineering Thermodynamics

4.15 How to Write a Thermodynamics Problem 135
A. Select the working equations and unknowns
The problem unknowns can be any of the variables carried within the basic laws of thermodynamics and any of
the related auxiliary equations introduced thus far. For simplicity, let us limit the discussion to a closed system
analysis. The general closed system energy balance is
1Q 2 − 1 W 2 = m ðu 2 − u 1 Þ + V2 2 − V2 1
2g c
and the general closed system energy rate balance is
_Q − _W = d
mu + mV2
dt 2g c
+ gðZ
2 − Z 1 Þ
g c
+ mgZ
g c
Any of the variables listed in these equations can be an unknown in a problem statement. In addition to the
basic balance equations, we have numerous auxiliary equations, such as
■
■
■
system
system
Equations of state for ideal gases, incompressible fluids, or other materials.
Process path equations such as polytropic, isobaric, and the like.
Various work mode equations for mechanical, electrical, and other work modes.
List all the basic (thermodynamics laws) and auxiliary equations you want the person who solves your problem
to use in the solution. Then choose the variables you want to use as unknowns. Remember, you need as many
independent equations in your list of equations as the number of unknowns you choose, so do not choose too
many. Then, assign numerical values to all the remaining variables in the equations that are to be used to solve
for the unknowns. Do not be too concerned about the actual values you pick at this point; if you choose the
wrong values, it will show up in step C, and you can correct them later.
B. Write a short story that contains all the information needed
to solve the problem
It would be helpful if we could categorize to some degree the wide variety of problem types or scenarios commonly
encountered in thermodynamics. The first classification is by the thermodynamic process used in the problem
scenario, the second classification is by the engineering technology used in the problem scenario, and the
third is by problem unknown. Since the number of variations within these classifications is quite large, they are
explained in detailed here.
Problem classification by thermodynamic process. A problem statement could involve more than one
process or involve unknown processes. Therefore, the process for changing the state of a system could be
the focal point of a problem statement. For example, we might want to find how the temperature
changes during a constant pressure process. This would then be the central theme of the problem
statement.
Problem classification by problem technology. The list of possible engineering technologies is much longer
than the list of known processes. Actually, any device or technology can be analyzed thermodynamically.
A series of “typical” technology based scenarios appear in engineering thermodynamics textbooks. For
example, you might want to find the work required to compress a gas with a piston, the change in
temperature across a nozzle, the power produced by a turbine, and so forth. Then, the problem statement
focuses on these technologies, providing numerical values for all the variables except the problem
unknowns.
Problem classification by problem unknown. These problems are usually the simplest, since they do
not depend on a specific technology or process path. The unknowns are simply calculated directly from
the thermodynamic laws (i.e., Q, W, KE, PE, etc.) or from an auxiliary equation (i.e., the ideal gas
equation, etc.).
C. Solve the problem in the forward direction
Here you (or a friend) must actually solve the problem you wrote using the data you provided in the problem
statement. You will usually find that you get stuck part way through the problem and have to go back
and modify the problem statement. That is OK, do it quickly and go on with the solution. Sometimes, values
you originally chose cannot be found easily in the tables or are unreasonable (for example, maybe you
wanted a state to be a vapor but the values you originally specified for pressure and temperature are for a
liquid). Using the tables in the tables book and your emerging solution, change the original values in your
problem statement so that the problem solution moves along smoothly. Be careful to check the units on each
calculation.