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Unformatted text preview: Homework Problems – Week 1 440:127 – Fall 2011 – S. J. Orfanidis This homework set is due online at Sakai no later than 5:00 AM on Wednesday, September 14, 2011. Late submissions will not be accepted. Please do the following problems: 1. Problem 2.7 of your textbook. In addition, please do the following. For the given values of P,n,a,b,R and for T = 1000 K, re-write the Van der Waals equation as a cubic equation in the variable V and put it in the polynomial form: c 1 V 3 + c 2 V 2 + c 3 V + c 4 = ⇒ c = [c 1 ,c 2 ,c 3 ,c 4 ] where we defined the vector of coefficients c . Derive expressions of the coefficients c i in terms of the parameters P,n,a,b,R,T , and calculate their numerical values. Then, using MATLAB’s built-in function roots , find the three solutions of this polynomial equation and decide which among them represents the physical value of V in liters. Compare that V with the one computed using the ideal gas law. Note that cubic equations can be solved exactly by algebraic formulas, like quadratic equations. We will look into that in another homework. We will also solve this problem using the functionlook into that in another homework....
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- Spring '11
- Quadratic equation, Elementary algebra, Cubic function, Mathematics in medieval Islam, maximum power transfer, Maximum power theorem