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Notes'.

Notes'.

The table starts at the triple point and ends at the critical point uf = 0 at the triple point is the reference internal eneigy but hf = 0.001 kJ/kg here sf = 0 at the triple point is the reference for the entropy u( and hg achieve maximum values at ~235°C

Example: Often, the quality is implicit in the specification of a problem. For example, suppose we want to calculate the quality of 2 kg of water contained in a vessel of 3 m3 volume at 75°C. The average specific volume of the mixture is v = 3/2 = 1.5 m3/kg, and at 75°C, the specific volumes of the individual phases are (from Table 2.2) vf= 0.001 m3/kg and v, = 4.12 m3/kg. Solving Equation (2.20) for x yields:

Overall conditions such as those in the above example must be approached with caution; the implicit assumption that two phases are present and that Table 2.2 is appropriate may not be valid. For instance if the mass of steam in the previous example were 0.5 kg instead of 2 kg, the mixture specific volume would have been 6 m3/kg. This value is greater than that of the saturated vapor, and application of Equation (2.20) would give x > 1, which is impossible. In this case, the conclusion is that the system is a singlephase superheated vapor, and Table 2.3 rather than Table 2.2 must be used. The use of Table 2.3 will be taken up in due course.

The steam tables provide complete thermal property data in the form of u, h, and s. Enthalpy data are presented even though this property can be computed from the pressure, volume and internal energy using the definition h - u + pv. The difference hfg - hg- hf is called the enthalpy of vaporization, and is an important thermodynamic property in its own right. In many problems, only hfg> and not fyand hg individually, is needed. In addition, hfg modestly simplifies the-calculation of average values in two-phase mixtures. Thus, the enthalpy of a liquid-vapor mixture of specified quality x is, by analogy to Equation (2.20), h = xhg + (1 - x)hf = hf+ xhfg (2.22)

The later form is somewhat easier to us.-

An interesting feature of the thermal-property data in Table 2.2 is die choice of reference states. In the discussion of u and h in Section 1.6, it was noted that either of these properties can be set equal to an arbitrary value at an arbitrary temperature and pressure, but both u and h cannot be so specified. Table 2.2 appears to violate this dictum because both uf and hf are equal to zero at the triple point <7*- 0.01 °C). If uf is taken as the reference value of zero, then hf at this condition should be 0 + (611.3 Pa)(0.001 m3/kg) = 0.61 J/kg, or 0.00061 kJ/kg. Since the tables provide Uf and hf in kJ/kg units only to three significant figures, listing hf at the triple point as 0.0 is not a contradiction.

The value of zero assigned to the entropy of liquid water in Table 2.2 appears to violate the third law of thermodynamics. This law states that the zero of entropy is attained only for crystalline solids at the absolute zero temperature. On this basis, the entropy of liquid water at 0.01 °C is clearly greater than zero. However, all calculations of thermodynamic processes involve differences in s (as well as of u and h), so the reference value chosen at the triple point cancels out. Again, the contradiction is not of practical importance.

Example: The average specific volume and enthalpy are given as v =0.12 m3/kg and h = 1500 kj/kg. To be determined is whether the system is in the two-phase region and if so, to calculate the quality and the temperature.

To solve this problem, a two-phase system is assumed. At a series of temperatures in Table 2.2, the quality is calculated by two methods.

jr(from v) = ——— «= — *(from h) = ——— vg-vf vg hg -hj

At each temperature, vg, vf, hf, and hf? are read from Table 2.2. The following table shows the details of the calculation.

T,°C

Getting Started With Solar

Getting Started With Solar

Do we really want the one thing that gives us its resources unconditionally to suffer even more than it is suffering now? Nature, is a part of our being from the earliest human days. We respect Nature and it gives us its bounty, but in the recent past greedy money hungry corporations have made us all so destructive, so wasteful.

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