3.6.1 Introducing Enthalpy
In many thermodynamic analyses the sum of the internal energy U and the product of pressure p and volume V appears. Because the sum U 1 pV occurs so frequently in subsequent discussions, it is convenient to give the combination a name, enthalpy, and a distinct symbol, H. By definition
H5U1pV (3.3)
Since U, p, and V are all properties, this combination is also a property. Enthalpy can be expressed on a unit mass basis
h5u1p𝜐 (3.4)
enthalpy
94 Chapter 3 Evaluating Properties and per mole
h5u1p𝜐 (3.5)
Units for enthalpy are the same as those for internal energy.
3.6.2 Retrieving u and h Data
The property tables introduced in Sec. 3.5 giving pressure, specific volume, and tem- perature also provide values of specific internal energy u, enthalpy h, and entropy s.
Use of these tables to evaluate u and h is described in the present section; the con- sideration of entropy is deferred until it is introduced in Chap. 6.
Data for specific internal energy u and enthalpy h are retrieved from the property tables in the same way as for specific volume. For saturation states, the values of uf
and ug, as well as hf and hg, are tabulated versus both saturation pressure and satura- tion temperature. The specific internal energy for a two-phase liquid–vapor mixture is calculated for a given quality in the same way the specific volume is calculated
u5 (12x)uf1xug5uf1x(ug2uf) (3.6) The increase in specific internal energy on vaporization (ug 2 uf) is often denoted by ufg. Similarly, the specific enthalpy for a two-phase liquid–vapor mixture is given in terms of the quality by
h5 (12x)hf1xhg5hf1x(hg2hf) (3.7) The increase in enthalpy during vaporization (hg 2 hf) is often tabulated for conve- nience under the heading hfg.
to illustrate the use of Eqs. 3.6 and 3.7, we determine the specific enthalpy of Refrigerant 22 when its temperature is 128C and its specific internal energy is 144.58 kJ/kg. Referring to Table A-7, the given internal energy value falls between uf and ug at 128C, so the state is a two-phase liquid–vapor mixture. The qual- ity of the mixture is found by using Eq. 3.6 and data from Table A-7 as follows:
x5 u2uf
ug2uf
5 144.58258.77 230.38258.7750.5 Then, with the values from Table A-7, Eq. 3.7 gives
h5(12x)hf1xhg
5(120.5)(59.35)10.5(253.99)5156.67 kJ/kg b b b b b
In the superheated vapor tables, u and h are tabulated along with 𝜐 as functions of temperature and pressure.
let us evaluate T, 𝜐, and h for water at 0.10 MPa and a specific internal energy of 2537.3 kJ/kg. Turning to Table A-3, note that the given value of u is greater than ug at 0.1 MPa (ug 5 2506.1 kJ/kg). This suggests that the state lies in the superheated vapor region. By inspection of Table A-4 we get T 5 1208C, 𝜐 5 1.793 m3/kg, and h 5 2716.6 kJ/kg. Alternatively, h and u are related by the definition of h
h5u1p𝜐 52537.3kJ
kg1a105N
m2ba1.793m3
kgb ` 1 kJ 103 N?m` 52537.31179.352716.6 kJ/kg
3.6 Evaluating Specific Internal Energy and Enthalpy 95 Specific internal energy and enthalpy data for liquid states of water are presented
in Tables A-5. The format of these tables is the same as that of the superheated vapor tables considered previously. Accordingly, property values for liquid states are retrieved in the same manner as those of vapor states.
For water, Tables A-6 give the equilibrium properties of saturated solid and satu- rated vapor. The first column lists the temperature, and the second column gives the corresponding saturation pressure. These states are at pressures and temperatures below those at the triple point. The next two columns give the specific volume of saturated solid, 𝜐i, and saturated vapor, 𝜐g, respectively. The table also provides the specific internal energy, enthalpy, and entropy values for the saturated solid and the saturated vapor at each of the temperatures listed.
3.6.3 Reference States and Reference Values
The values of u, h, and s given in the property tables are not obtained by direct measurement but are calculated from other data that can be more readily determined experimentally. The computational procedures require use of the second law of ther- modynamics, so consideration of these procedures is deferred to Chap. 11 after the second law has been introduced. However, because u, h, and s are calculated, the matter of reference states and reference values becomes important and is consid- ered briefly in the following paragraphs.
When applying the energy balance, it is differences in internal, kinetic, and poten- tial energy between two states that are important, and not the values of these energy quantities at each of the two states.
consider the case of potential energy. The numerical value of potential energy determined relative to the surface of the earth is not the same as the value relative to the top of a tall building at the same location. However, the differ- ence in potential energy between any two elevations is precisely the same regardless of the datum selected, because the datum cancels in the calculation.b b b b b
Similarly, values can be assigned to specific internal energy and enthalpy relative to arbitrary reference values at arbitrary reference states. As for the case of potential energy considered above, the use of values of a particular property determined rela- tive to an arbitrary reference is unambiguous as long as the calculations being per- formed involve only differences in that property, for then the reference value cancels.
When chemical reactions take place among the substances under consideration, spe- cial attention must be given to the matter of reference states and values, however. A discussion of how property values are assigned when analyzing reactive systems is given in Chap. 13.
The tabular values of u and h for water, ammonia, propane, and Refrigerants 22 and 134a provided in the Appendix are relative to the following reference states and values. For water, the reference state is saturated liquid at 0.018C (32.028F). At this state, the specific internal energy is set to zero. Values of the specific enthalpy are calculated from h 5 u 1 p𝜐, using the tabulated values for p, 𝜐, and u. For ammonia, propane, and the refrigerants, the reference state is saturated liquid at 2408C. At this reference state the specific enthalpy is set to zero. Values of specific internal energy are calculated from u 5 h 2 p𝜐 by using the tabulated values for p, 𝜐, and h. Notice in Table A-7 that this leads to a negative value for internal energy at the reference state, which emphasizes that it is not the numerical values assigned to u and h at a given state that are impor- tant but their differences between states. The values assigned to particular states change if the refe rence state or reference values change, but the differences remain the same.
reference states reference values
96 Chapter 3 Evaluating Properties