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:
For a control volume/open system:
6. Apply conservation of energy to process (1st law of thermodynamics)
For a control mass/closed system:
(equilibrium process)
(transient process)
For a control volume/open system:
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”
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 / EquationConduction (C & T ch 15-16) /
Convection (C & T ch 17 – 18) /
Radiation (C & T ch 19) /
Catalog of Work
Work Mode / EquationElectric (C & T ch 4.2) /
Spring (C & T ch 4.3.3) /
Shaft (C & T ch 4.3.2) /
Expansion/Compression (C & T ch 4.3.1) /
Bar Deformation (C & T ch 4.3.4) /
Surface Tension (C&T ch 4.3.4) /
Catalog of Steady Flow Devices
Device / Conversion Process / Typical AssumptionsNozzle (C&T ch 5.4.1)
Diffuser / Flow energy(T, P) to KE
KE to flow energy (T, P) / S.S., adiabatic, no work, DPE = 0
Turbine (C&T ch 5.4.2)
Compressor
Pump / Flow energy (T, P) to work
Work to flow energy (T, P)
Work to flow energy (P) / S.S, adiabatic, DKE » DPE » 0
Throttle Device (C&T ch 5.4.3) / Relieve pressure / S.S., adiabatic, no work, DKE » DPE » 0
Heat Exchanger (C&T ch 5.4.4) / Transfer heat between flow streams / S.S., no work, DKE » DPE » 0, external surfaces adiabatic
Catalog of Substance Models
Property Tables – solid, liquid, vapor (C&T ch 3.6) / Whenever experimental data is available for substance of interest / Real data, so this is ideal as long as the experimental conditions used to make table are broadly applicable to the application.
Incompressible – liquid (C&T ch 3.6.3 and ch 3.11) / Most liquids and processes where volume expansion is not of interest (an example of a mis-application would be a natural convection process) / Properties are approximated by the saturated liquid properties at the system temperature. Specific heats are temperature dependent only.
Cp = Cv = C
du = CdT = f(T)
y » yf(T)
h » hf(T) + vf(T)*[p – psat(T)]
Incompressible – solid (C&T ch 3.6.3 and ch 3.11) / Most solids and processes where volume expansion is not of interest (an example of a mis-application would be a deformation/bar expansion process) / Specific heats are temperature dependent only.
Cp = Cv = C
du = CdT = f(T)
Compressibility Chart (Principle of Corresponding States)- vapor (C & T ch 3.7) / Vapors that cannot be classified as an ideal gas / 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
Ideal Gas (C & T ch 3.7, ch 3.10) / Special case vapor where PR (P/Pcrit) is nearly 0. / 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)
Gary L. Solbrekken ME3324, Fall 2002 10/01/02