Thermodynamic Data It is not possible to know the absolute value of U ˆ or H ˆ for a pure substance, but you can determine the change in U ˆ ( U ˆ ) or Hˆ ( Hˆ ) corresponding to a specified change of state (temperature, pressure, and phase). The change is actually often what we want to know. A common practice is to arbitrarily designate a reference state for a substance at which U ˆ and H ˆ are arbitrarily set to be equal to zero, and then tabulate U ˆ and/or H ˆ for the substance relative to the reference state. For example, ˆ CO (g, 0C, 1 atm) CO (g,100C, 1 atm): HCO 2919 J/mol ˆ ˆ reference state HCO HCO 0 2919 J/mol We say: “The specific enthalpy of CO at 100C and 1 atm relative to CO at 0C and 1 atm is 2919 J/mol”. CHEE 221 1 Reference States and State Properties Most (all?) enthalpy tables report the reference states (T, P and State) on which the values of H ˆ are based; however, it is not necessary to know the reference state to calculate H (change in enthalpy) for the transition from one state to another. ˆ ˆ –H from state 1 to state 2 equals H 2 H 1 regardless of the reference state upon which ˆ and ˆ were based H1 H 2 – Caution: If you use different tables, you must make sure they have the same reference state This result is a consequence of the fact that H ˆ (and U ˆ ) are state properties, that is, their values depend only on the state of the species (temperature, pressure, state) and not on how the species reached its state. When a species passes from one state to another, both U ˆ and H ˆ for the process are independent of the path taken from the first state to the second one. CHEE 221 2 Example 7.5-1 The following entries are taken from a data table for saturated methyl chloride: ˆ 3/ ˆ State T(F) P (psia) V (ft lbm ) H (Btu/lbm ) Liquid -40 6.878 0.01553 0.000 Vapour 0 18.90 4.969 196.23 Vapour 50 51.99 1.920 202.28 1. What reference state was used to generate the given enthalpies? 2. Calculate H ˆ and U ˆ for the transition of saturated methyl chloride vapour from 50F to 0F. CHEE 221 3 Steam Tables Tables located in the back of F&R can be used to estimate U ˆ , Hˆ and Vˆ for liquid water and steam (water vapour) at any specified temperature and pressure. Recall the phase diagram for water: Vapour-liquid equilibrium (VLE) curve or saturation line – water may Subcooled liquid exist as saturated water, saturated steam (vapour) or mixture of both. superheated steam CHEE 221 4 Steam Tables Saturated Steam Tables: Data taken along the VLE curve or saturation line. Table B.5 Saturated Steam: Properties of saturated water and saturated steam as a function of temperature from 0.01C (triple point) to 102C. Note boiling points at various P values and vapour pressures at T values. Table B.6 Saturated Steam: Properties of saturated water and saturated steam as a function of pressure (same data as Table B.5 but over a much larger range of temperatures and pressures). Superheated Steam Table: Data taken from points below the VLE curve or saturation line – vapour heated above its saturation temperature. Table B.7 Superheated Steam: Properties of superheated steam at any temperature and pressure – includes data for liquid water (data in the enclosed region), and saturated water and saturated steam. CHEE 221 5 Notes on the Steam Tables Reference state for the tabulated thermodynamic data in the steam tables is liquid water at the triple point (0.01C and 0.00611 bar) [triple point is where all three phases of water can coexist] kJ kJ Units are on a mass basis: Uˆ and Hˆ kg kg Heat of vapourization (evaporation) is the difference between vapour and liquid enthalpies Properties of liquid water are not a strong function of pressure at constant temperature, therefore H ˆ U ˆ since volume change is small Volumetric properties of steam are extensively tabulated: when steam tables are available, don’t use the ideal gas law. Remember: Hˆ (P,T ) Uˆ PVˆ CHEE 221 6 Steam Tables – Interpolation Sometimes you need to an estimate of specific enthalpy, specific internal energy or specific volume at a temperature and pressure that is between tabulated values (Usually B7) Use linear interpolation: use this equation to estimate y for an x between x0 and x1 –E.g.; superheated steam at 20 bar, with enthalpy of 3065 kJ/kg. What T is the steam at? –Steam at 400 °C and 25 bar. What is the specific enthalpy? CHEE 221 7 Example 7.5-2 1. Determine the vapour pressure, specific internal energy, and specific enthalpy of saturated steam at 133.5C. 2. Show that water at 400C and 10 bar is superheated steam and determine its specific volume, specific internal energy, and specific enthalpy relative to liquid water at the triple point. 3. Show U ˆ and H ˆ for superheated steam depend strongly on temperature and relatively slightly on pressure. CHEE 221 8 Example Steam at 80 bar absolute with 155C of superheat is fed to a turbine at a rate of 2000 kg/h. The turbine operation is adiabatic, and the effluent is saturated steam at 1 bar. Calculate the work output of the turbine in kilowatts, neglecting kinetic and potential energy changes. CHEE 221 9 Example 7.6-3 Saturated steam at 1 atm is discharged from a turbine at a rate of 1150 kg/h. Superheated steam at 300C and 1 atm is needed as a feed to a heat exchanger; to produce it, the turbine discharge stream is mixed with superheated steam available from a second source at 400C and 1 atm. The mixing unit operates adiabatically. Calculate the amount of superheated steam at 300C produced and the required volumetric flow rate of the 400C steam. CHEE 221 10 Problem 7.26 F&R Liquid water is fed to a boiler at 24C at 10 bar and is converted at constant pressure to saturated steam. Use the steam tables to calculate H ˆ ( kJ / kg ) for this process, and then calculate the heat input required to produce 15,000 m3/h of steam at the exiting conditions. Assume that the kinetic energy of the entering liquid is negligible and that the steam is discharged through a 15 cm ID (inner diameter) pipe. CHEE 221 11.