Thermodynamic Data It is not possible to know the absolute value of Uˆ or Ĥ for a pure substance, but you can determine the change in U ˆ ( U ˆ ) or H ˆ ( 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 Uˆ and Ĥ are arbitrarily set to be equal to zero, and then tabulate Uˆ and/or Ĥ for the substance relative to the reference state. For example, CO (g, 0 C, 1 atm) CO (g,100 C, 1 atm): reference state Hˆ ˆ CO H CO 0 2919 J/mol CHEE 221 1 Ĥ CO 2919 J/mol We say: The specific enthalpy of CO at 100 C and 1 atm relative to CO at 0 C and 1 atm is 2919 J/mol.
Reference States and State Properties Most (all?) enthalpy tables report the reference states (T, P and State) on which the values of Ĥ 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. H from state 1 to state 2 equals Hˆ regardless of the 2 Hˆ 1 reference state upon which Ĥ and were based 1 Ĥ 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 Ĥ (and Uˆ ) 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 Uˆ and Ĥ 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: State T( F) P (psia) Ĥ (Btu/lb m ) 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 Ĥ and Uˆ for the transition of saturated methyl chloride vapour from 50 F to 0 F. Vˆ (ft 3/ lb m ) CHEE 221 3
Steam Tables Tables located in the back of F&R can be used to estimate Uˆ, and V ˆ for liquid water and steam (water vapour) at any specified temperature and pressure. Ĥ Recall the phase diagram for water: Subcooled liquid superheated steam Vapour-liquid equilibrium (VLE) curve or saturation line water may exist as saturated water, saturated steam (vapour) or mixture of both. 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 0.01 C (triple point) to 102 C. 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 (0.01 C and 0.00611 bar) [triple point is where all three phases of water can coexist] Units are on a mass basis: 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 Ĥ Û 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 U ˆ PVˆ kj and H ˆ kj 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 x 0 and x 1 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 133.5 C. 2. Show that water at 400 C 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 Uˆ and Ĥ for superheated steam depend strongly on temperature and relatively slightly on pressure. CHEE 221 8
Example Steam at 80 bar absolute with 155 C 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 300 C 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 400 C and 1 atm. The mixing unit operates adiabatically. Calculate the amount of superheated steam at 300 C produced and the required volumetric flow rate of the 400 C steam. CHEE 221 10
Problem 7.26 F&R Liquid water is fed to a boiler at 24 C at 10 bar and is converted at constant pressure to saturated steam. Use the steam tables to calculate Hˆ ( kj / kg) for this process, and then calculate the heat input required to produce 15,000 m 3 /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