Solving Thermodynamics Problems
Solving thermodynamic problems can be made significantly easier by following a
rigorous process. One such process is outlined below.
1. Summarize given data in own words, leaving out unneeded, misleading information
2. Clearly understand/identify what is being asked for – draw a sketch showing
interactions and identify a solution strategy, keeping in mind that a multi-step
approach may be easiest.
3. Define system boundaries, noting if it is an open or closed system
4. Fix as many states as possible on a P-v/T-v/T-s diagram using given information
5. Apply conservation of mass to process
For a control mass/closed system:
m 2  m1  0
For a control volume/open system:
dm
 i  m
e
 m
dt
6. Apply conservation of energy to process (1st law of thermodynamics)
For a control mass/closed system:
E  Q  W (equilibrium process)
dE  
 QW
dt
(transient process)
For a control volume/open system:




dE  
V2
V2
 i  h 
 e  h 
 Q W  m
 gz    m
 gz 
dt
2
2

i

e
7. Solve algebraically for desired quantity using combination of mass balance, energy
balance, and definitions (like mass flow rate, volume, etc.)
8. Perform heat transfer analysis to get Q, if necessary (use catalog of heat transfer or
steady flow device in appendix)
9. Perform work analysis to get W, if necessary (use catalog of work or steady flow
device in appendix)
10. Assume appropriate model for system substance (use substance model catalog in
appendix)
11. Find properties using substance model
12. Substitute numbers into equation and solve for desired quantity
13. Sanity check magnitude of answer and direction (if any) to see if the solution “makes
sense”
Gary L. Solbrekken
ME3324, Fall 2002
10/01/02
Appendix
This appendix contains a series of catalogs for common parameters that are needed in
solving thermodynamics problems. The lists are not intended to be exhaustive, nor is the
information contained in the catalogs complete. For a complete discussion of a particular
entry, a reference from the Cengel and Turner (C&T) book is included with the chapter
and section identified. Note that the symbols used take on the context of the problem.
Again, the user should consult C&T for details.
Catalog of Heat Transfer
Heat Transfer Mode
Conduction (C & T ch 15-16)
Equation
  kA dT
Q
dx

Q  hA Twall  Tambient 
  F A T 4  T 4
Q
Convection (C & T ch 17 – 18)
Radiation (C & T ch 19)

12
1
2

Catalog of Work
Work Mode
Electric (C & T ch 4.2)
Spring (C & T ch 4.3.3)
Equation
W  VIt
1
W  k x 22  x12
2
W  2n

Shaft (C & T ch 4.3.2)
Expansion/Compression (C & T ch 4.3.1)

W   PdV
Bar Deformation (C & T ch 4.3.4)
W   A o L o d
Surface Tension (C&T ch 4.3.4)
W   dA
Catalog of Steady Flow Devices
Device
Conversion Process
Nozzle (C&T ch 5.4.1)
Flow energy(T, P) to KE
Diffuser
KE to flow energy (T, P)
Turbine (C&T ch 5.4.2)
Flow energy (T, P) to work
Compressor
Work to flow energy (T, P)
Pump
Work to flow energy (P)
Throttle Device (C&T ch Relieve pressure
5.4.3)
Heat Exchanger (C&T ch Transfer heat between flow
5.4.4)
streams
Gary L. Solbrekken
ME3324, Fall 2002
Typical Assumptions
S.S., adiabatic, no work,
PE = 0
S.S, adiabatic, KE  PE
0
S.S., adiabatic, no work,
KE  PE  0
S.S., no work, KE  PE
 0, external surfaces
adiabatic
10/01/02
Catalog of Substance Models
Substance Model
Application Domain
Characteristics
Property Tables – solid, Whenever
experimental Real data, so this is ideal as
liquid, vapor (C&T ch 3.6)
data is available for long as the experimental
substance of interest
conditions used to make
table are broadly applicable
to the application.
Incompressible – liquid Most liquids and processes Properties are approximated
(C&T ch 3.6.3 and ch 3.11) where volume expansion is by the saturated liquid
not of interest (an example properties at the system
of a mis-application would temperature. Specific heats
be a natural convection are temperature dependent
process)
only.
Cp = Cv = C
du = CdT = f(T)
y  yf(T)
h  hf(T) + vf(T)*[p – psat(T)]
Incompressible – solid Most solids and processes
(C&T ch 3.6.3 and ch 3.11) where volume expansion is
not of interest (an example
of a mis-application would
be
a
deformation/bar
expansion process)
Compressibility
Chart Vapors that cannot be
(Principle of Corresponding classified as an ideal gas
States)- vapor (C & T ch
3.7)
Ideal Gas (C & T ch 3.7, ch Special case vapor where PR
3.10)
(P/Pcrit) is nearly 0.
Gary L. Solbrekken
ME3324, Fall 2002
Specific
heats
are
temperature
dependent
only.
Cp = Cv = C
du = CdT = f(T)
Assumes that the vapors of
all
substances
are
qualitatively
similar,
relative to their critical
state. Scaling relative to the
critical state allows the
generalized compressibility
chart to be used to find
relation between P-v-T.
Z = Pv/RT
PR = P/Pcrit
TR = T/Tcrit
Allows use of ideal gas
equation of state, PV =
mRT. Also, specific heats
are
only
temperature
dependent,
meaning
energies are also only
functions of temperature
du = CvdT = f(T)
dh = CpdT = f(T)
10/01/02