Thermodynamic Property Tables Property Tables

• If you have 2 properties, • There are separate property you can find the others tables for saturated using the mixtures, subcooled liquids, thermodynamic property superheated vapors, and tables. ideal gases.

• E.g. If you have pressure • Thermodynamic property and for tables can be found in the steam, you can find it’s back of your textbook or specific volume, various places online. , internal , and entropy. Interpolation

• Interpolation allows you to find • E.g. If a subcooled liquid has a values that are in between what known pressure of 3.0 kPa, and a the table provides temperature of 27°C, but the only • The interpolation factor is listed on the chart consistent throughout the table are 20°C and 30°C, then the for each individual state and is interpolation factor is: T  T 27  20 given by: a  l   0.7 Th  Tl 30  20 v  vl a  • Other properties are found by: v  v h l v  vl  a * (v h  vl ) where v is the actual (given) u  u  a * (u  u ) property value, vl is the lower l h l h  h  a * (h  h ) value on the chart, and vh is the l h l higher value on the chart.

Saturated Property Tables

• Between a liquid and a • To determine whether or vapor – contains both. not a substance is a • Quality (0 ≤ x ≤ 1) saturated mixture from the determines properties. pressure and temperature, • A quality of 0 is a saturated look at the pressure charts. liquid. • If the temperature of the • actual substance is higher A quality of 1 is a saturated than the saturated vapor. temperature, it’s a • If given a temperature and superheated vapor. a pressure, the quality is • needed to determine its If it’s lower, it’s a subcooled other properties. liquid. • If the two temperatures are equal, it is a saturated mixture.

Temperature Tables

• Use the temperature table for when you are given the temperature of a saturated mixture • Use the temperature and the quality to determine the other properties • E.g. For steam at 70°C and a quality of 0.25, the specific volume is:

v  v f  x * (v g  v f ) v  .00102  .25 * (5.0395  .00102 )

3 v  1.2606 m kg Temperature Tables

• If given temperature and another property, find the quality by reversing the process. • E.g. For steam at 70°C and a specific energy of 1000kJ/kg:

u  u f x  u g  u f 1000  293 .03 x  2468 .9  293 .03 x  0.325 • The pressure for any saturated mixture is the pressure at that temperature

Pressure Tables

• Use the pressure table for when you are given the pressure of a saturated mixture • Like the temperature table, use the pressure and the quality to determine the other properties • E.g. For R134a at 300kPa and a quality of 0.25, the specific volume is: v  v  x * (v  v ) f g f v  .0007737  .25 * (.0677  .0007737 )

3 v  .0175 m kg Superheated Gas Tables

• Used for temperatures higher than the saturation temperature at a given pressure. • Any two properties allow you to find all other properties at that state. • E.g. For superheated R744 at 100° and h=558 kJ/kg, the pressure is: h  h a  l hh  hl 558  554 .73 a   0.524 560 .97  554 .73

P  Pl  a * ( Ph  Pl ) P  3.0  .524 * (2.0  3.0) P  2.48 MPa Subcooled Liquid Tables • Used for temperatures lower than the saturation temperature at a given pressure • Any two properties allow you to find all other properties at that state. • E.g. For subcooled at 240°C and u=1027 KJ/kg, the pressure is: u  u a  l u h  u l 1027  1026 .1 a   0.164 1031 .6  1026 .1

P  Pl  a * ( Ph  Pl ) P  10 .0  .164 * (5.0  10 .0) P  9.18 MPa References

Fundamentals of Engineering Thermodynamics, Moran and Shapiro, Ch.3

Thermodynamics – Theory http://ecourses.ou.edu/cgi- bin/ebook.cgi?doc=&topic=th&chap_sec=02.3&page=theory

Steam Tables – Thermodynamics http://www.engineersedge.com/thermodynamics/steam_tables.ht m

Guide to Using the Two-Phase Property Tables http://abata.sdsmt.edu/pdf_files/ME211/Guide%20to%20Using%20 the%20Two%20Phase%20Property%20Tables.pdf

Prepared by Veronica Hannink