Modern Engineering Thermodynamics

4.14 A Thermodynamic Problem Solving Technique 133
Step 4. Now identify the process connecting the state or stations. The process path statement is usually given
in technical terms such as a closed, rigid vessel, meaning an isochoric (or constant volume) process will occur.
Proper identification of the process path is very important, because it often provides numerical values for state
properties (e.g., v 2 = v 1 for a closed, rigid vessel) or heat, work, or other thermodynamic quantities (e.g., an
insulated or adiabatic system has 1 Q 2 = _Q = 0, an aergonic system has 1 W 2 = _W =0, and so forth). When two
independent property values are given in the problem statement for each state or station of the system, the
process path is not necessary unless it provides values for heat, work, kinetic energy, or potential energy.
Step 5. Write down all the basic equations. Your work sheet should now have all the details of the
problem on it and you should not have to look at the problem statement again. The actual solution to the
problem is begun by automatically writing down (whether you think you need them or not) all the relevant
basic equations. Thermodynamics has only three basic equations:
a. The conservation of mass (which is also called the mass balance).
b. The first law of thermodynamics (which is also called the energy balance or the conservation of energy).
c. The second law of thermodynamics (which is also called the entropy balance).
In closed systems, the conservation of mass is automatically satisfied and need not be written down. Also, since
the entropy balance is not be introduced until Chapter 7, it does not enter into the solution of any problems until
then. So, for solving the closed system problems of Chapter 5, there is really only one relevant basic equation: the
first law of thermodynamics. In solving the open system problems of Chapter 6, there are two relevant basic
equations: the conservation of mass and the first law of thermodynamics.
Write any necessary auxiliary equations. All the equations developed in this book that are not one of the
three basic equations discussed previously are called auxiliary equations. For example, all equations of state
(ideal gas and incompressible materials), all work mode equations (mechanical, electrical, etc.), all heat
mode equations (conduction, convection, radiation), all property-defining equations (specific heats,
The easiest way to show the process path on your work sheet is to write the statement “Process: process name” on a connecting
arrow between the state or station data sets. In the closed system example used in step 3, if the state change occurs in a
closed, rigid vessel and we do not know the final quality, then we would write
Process: v = constant
State 1 ƒƒƒƒƒƒƒƒƒƒ! State 2
p 1 = 14:7 psia
p 2 = 200: psia
v 1 = 0:500 ft 3 /lbm v 2 = v 1 = 0:500 ft 3 /lbm
And, if the open system of step 3 is operated at a constant pressure (i.e., an isobaric process) and we do not know the final
quality, then we would write
Process: p = constant
ƒƒƒƒƒƒƒƒƒƒ!
Station 1
Station 2
p 1 = 1:00 MPa v 2 = 26:3m 3 /kg
T 1 = 300:°C p 2 = p 1 = 1:00 MPa
Always write down the complete general form of the basic equations. Do not try to second-guess the problem by writing
the shorter specialized forms of the basic equations that were developed for specific applications. Then, cross out all terms
that vanish as a result of given constraints or process statements. For example, for a closed, adiabatic, stationary system, we
write the energy balance as (see Eq. (4.20), where we have used the abbreviation KE = mV 2 /2g c and PE = mgZ/g c )
⎵
1 Q 2 − 1 W 2 = mðu 2 − u 1 Þ + KE 2 − KE 1 + PE 2 − PE 1
⎵
j
= 0 ðadiabatic ðinsulatedÞ systemÞ
= 0 ðstationary - i.e., not moving)
Notice that we write why each crossed out term vanishes (“adiabatic” and “stationary” in this case). This makes the
solution easier to follow and to check later if the correct answer was not obtained.