The entire chapter is required reading, except for Section 2.6 "Equations of State for a Nonideal Gas". We will always use the Compressibilty Factor (Z) when dealing with a nonideal gas.
We recommend that you attempt the following
eleven Supplementary Problems: 2.12, 2.14, 2.15, 2.16, 2.18. 2.19,
2.21, 2.24, 2.26, 2.28, 2.30. All answers to the Supplementary
Problems are given at the end of the chapter, however we would
like you to revise the following problems/answers:
2.19 - Replace temperature 140°C in the problem with 150°C.
The correct answers are: (a) 413 kPa, (b) 263 kPa. (Note:
compare these results with those using the ideal gas equation
of state (Rsteam = 0.4615 [kJ/kg K]) and determine the % error
in each case)
2.21 - Replace the word "steam" with "R134a refrigerant".
The correct answer is 0.79 MPa.
2.30 - You will need to evaluate the the compressibility factor
Z for both cases to correctly solve this problem - refer to Replacement
Example 2.7 below. The correct answers are: (a) 190 kg (Z = 0.98),
(b) 500 kg (Z = 0.74).
This chapter covers the use of Steam Tables,
Refrigerant R134a Tables, and the Ideal Gas Equation of State.
At this stage we have found three typos in the Steam tables, as
follows:
1. Page 356, first row group, third column (0.10 MPa - replace
h at 500°C (3483.1 kJ/kg) with 3488.1 kJ/kg.
2. Page 357, second row group, third column - replace the header
[P = 1.80 MPa (207.15°C)] with [P = 2.00 MPa (212.4°C)].
3. Page 358, third row group - replace the temperature T = 406°C
with 400°C.
We will cover all of the examples presented by Potter and Somerton in detail in class. The equation development in Example 2.6 will be redone and extended to include the performance of a hot air balloon, and Example 2.7 will be replaced with a more suitable example. Both examples are presented below.
Potter Example 2.6
(repeated here for convenience): The temperature in the atmosphere
near the surface of the earth (up to an elevation of 10000m) can
be approximated by T(z) = 15 - 0.00651z°C. Determine the pressure
at an elevation of 3000 m if at z = 0, P = 101 kPa.
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We feel that the solution can be developed in a much more intuitive manner than that developed by Potter and Somerton, by using the hydrostatic equation, the equation of state, and the lapse rate, as follows:
This is identical to the result presented by Potter and Somerton. You may wonder why we would be interested in knowing the value of air pressure at 3000 m altitude. In the following example we continue with the above development in order to evaluate the payload that can be lifted to an altitude of 3000 m using a small hot air balloon (Volume =1000 m3).
Finally - with 154 kg payload at least 2 persons can share and enjoy this wonderful experience, however they will not be able to enjoy a decent cup of English tea. At a pressure of 69.9 kPa water will boil at (heavens forbid) < 90°C! (Saturation temperature Tsat from the Steam Tables). As an exercise, determine the temperature of a cup of tea in Denver, Colorado (elevation 5000 ft), or on the peaks of the Rocky Mountains (elevation 14000 ft. Hint: use the Units Survival Kit to first convert from feet to meters)
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Potter Example 2.7 This example evaluates the non-ideal gas equations of state, using steam as an example. We would prefer to use an example of an ideal gas that we are all familiar with (nitrogen) operated in a region where it exibits non-ideal behaviour. This will give us familiarity with using the Generalized Compressibility Chart. We find it strange that Potter presents a logarithmic compressibility chart in the text (Figure 2-6), however presents a sequence of linear generalized charts in the Appendix G. We prefer to use the Lee-Kessler (logarithmic) Compressibilty Chart, which should be used exclusively for solving this type of problem.
Replacement Example 2.7 Determine the specific volume (v) of nitrogen gas at 8 MPa and 150 K based on (a) the experimental value from nitrogen tables (v = 0.0029107 m3/kg), (b) the ideal gas equation, and (c) the generalized compressibility chart. Compare (b) and (c) to (a) and determine the error in each case.
This example is plotted on the Lee-Kesler Compressibility Chart as follows:
Obviously this is a contrived example, however the general rule is that if P << PCR or if T >> TCR then you are probably dealing with an ideal gas. If in doubt always check the Compressibility Factor Z on the Compressibility Chart.
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