Modern Engineering Thermodynamics

132 CHAPTER 4: The First Law of Thermodynamics and Energy Transport Mechanisms
WHAT IS THE SECRET TO SOLVING THERMODYNAMICS PROBLEMS?
The secret to solving thermodynamic problems is to do the analysis first and do the calculations last, not the other way around.
The basic process for solving a thermodynamics problem is this:
Begin by carefully reading the problem statement completely through.
Step 1. Make a sketch of the system and put a dashed line around the system boundary.
Step 2. Identify the unknown(s) and write them on your system sketch.
Step 3. Identify the type of system (closed or open) you have.
Step 4. Identify the process that connects the states or stations.
Step 5. Write down the basic thermodynamic equations and any useful auxiliary equations.
Step 6. Algebraically solve for the unknown(s).
Step 7. Calculate the value(s) of the unknown(s).
Step 8. Check all algebra, calculations, and units.
The process is this:
Sketch ! Unknowns ! System ! Process ! Equations ! Solve ! Calculate ! Check
For example, if you have a closed system that is initially at 14.7 psia with a specific volume of 0.500 ft 3 /lbm and by some
process it ends up at 200. psia at a quality of 90.0%, you should write this information on your work sheet in the following
form (always be sure to include the units on these values):
Process path
State 1 ƒƒƒƒƒ! State 2
p 1 = 14:7 psia p 2 = 200: psia
v 1 = 0:500 ft 3 /lbm x 2 = 0:900
For example, if you have a flow stream entering the system at station 1 with a temperature of 300.°C andapressureof
1.00 MPa, and a flow stream exiting the system at station 2 with a specific volume of 26.3 m 3 /kg and a quality of 99.0%,
you should write this information on your work sheet as (always be sure to include the units on these values):
Process path
Station 1
ƒƒƒƒƒ! Station 2
p 1 = 1:00 MPa v 2 = 26:3m 3 /kg
T 1 = 300:°C x 2 = 0:990
Here, too, we are trying to identify two independent property values at each station, because in simple systems, they fix the
state of the material at that station.
Notice that, for “simple” thermodynamic systems, we always are looking for the values of two independent
properties in each state. These two property values fix (i.e., determine) the state and we can then find the values
of any of the other properties needed at that state.
Often a problem statement gives only one property value at a system state. In this case, the remaining independent
property value at that state is usually given by the process path statement that indicates how that state was
achieved (e.g., an isothermal process tells us that T 2 = T 1 ) or else it may be a problem unknown to be
determined.
If it is an open system, we are interested in any changes that occur in the system bulk properties of the system
plus all the properties of the entering and exiting flow streams. Flow stream properties are referred to as monitoring
station properties, to clearly separate them from bulk system properties.