110124_Homework3

110124_Homework3 - 1/2 , where m is the weight of a gas...

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Chem340 Physical Chemistry for Biochemists Dr. Yoshitaka Ishii Homework 3 Due Date Feb 2, 2011 P2.3, P2.7, P2.11, P2.12, P2.15, P2.19, P2.20, P2.23, P2.25, P2.26, P2.29, P2.43 1. Calculate dy/dx for the following y: (a) y =ax +b; (b) y =2x 2 ; (c) y = 3x 5 + 2(x+a) -3 (d) y = ln(x/a); (e) y = C exp(-ax); (f) y= Acos(x) (g) y= Asin(bx) +Ccos(x/b) (h) y = x 2 exp(-ax 2 ) 2. Calculate dy/dx from the following equations (a) ln(x) + y = xy (b) 1 = cos(x)y 3.  3 2 2 2 4 Z kT C m C C P / exp ) ( . (a) Calculate dP(C)/dC. (b) Show there two solutions for dP(C)/dC = 0 (C 0) and one solution gives the most probable speed, C = (2RT/M)
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Unformatted text preview: 1/2 , where m is the weight of a gas molecule, M is its molar mass, and k is the Boltzmann constant. 4. Calculate f/ x and f/ y for the following f (x, y): (a) f = x-2 y 3 (b) f = sin(3xy) (c) f = ln(xy 3 ) (d) f = y 2 x 4 + y 2 exp(-xy 2 ). 5. Calculate C v = ( U/ T) V and C p = { (U + PV)/ T} P for n mole of ideal gas assuming that U = 5nRT/2 and n is a constant. What kind of molecular properties do they depend on? Hint: If you find a trouble in differential calculations, please read Appendix A2 (A2.1-A2.3). Partial derivatives are summarized in A.6....
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