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Unformatted text preview: Double Interpolation Two (independent) properties fix the state of a simple, pure substance. How many times have I made this point? Sometime in the future (hopefully near future) students of thermodynamics will rely exclusively on computerized thermodynamic property software to implement the two–property principle. Until then, the property tables will be the primary source of property information, and to use these tables the student must be proficient in interpolation methods. Here is an example of a double interpolation problem: Find P for water at T = 323 ◦ C, v = 0 . 2 m 3 / kg : This is a superheated state since v > v g (323 ◦ C). The temperature lies between listings for 300 and 350 ◦ C in the superheated tables. By inspection, we arrive at the following data points: P , kPa T, ◦ C v, m 3 / kg 1200 300 0.2134 1200 350 0.2345 1400 300 0.1823 1400 350 0.2003 Note that by ‘eyeballing’ the numbers, we can see that the volume for the first pair, at 323 ◦ C, will be somewhat larger that 0.2 m 3 / kg, and the volume for the second pair will be smaller. Our sought data point will therefore be bracketed by the four listed points. Now interpolate using the first pair of data points to get v for 1200 kPa and 323 ◦ C. The general formula is y = y 1 + ( y 2- y 1 ) x- x 1 x 2- x 1 in which x is what we know, y is what we’re after, and subscripts 1 and 2 denote data point values....
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- Fall '11
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