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 temperature for tables can be found in the steam, you can find it’s back of your textbook or specific volume, various places online. enthalpy, internal energy, 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 temperatures 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 water 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