Solutions set 3 - Problem Set#3 Assigned September 6 2013 Due Friday Please show all work for credit To warm up or practice try the Atkins Exercises

Solutions set 3 - Problem Set#3 Assigned September 6 2013...

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Problem Set #3 Assigned September 6, 2013 – Due Friday, September 13, 2013 Please show all work for credit To “warm up” or practice try the Atkins Exercises, which are generally simple one step problems Partial Derivatives 1. Engle – P. 3.2 (First and second partial derivatives)   lny y x 2 y Cos e x 12 5x Sin y 5x Cos x y 5 x f 2 2x y .   y Sin e 3 y 2 lny x y x 5x Sin x y f 2 2x 2 2 x     lny y 2 y Cos x e 48 y Cos e 12 5x Sin x y 25 5x Cos y 10 x f 2 2x 2x y 2 2 2 2   2 3 2 4y lny x - y Cos e 3 y f 2 2x x 2 2   y Sin x e 12 x 5 Cos x 5 5x Sin y lny x y x 2 y f x f 2 2x x y a)   y x 2x x y y f x f 5x Sin y lny x y x 2 y Sin x e 12 x 5 Cos x 5 x f y f 2 b)     dy y Sin e 3 y 2 lny x y x 5x Sin x dx lny y x 2 y Cos e x 12 5x Sin y 5x Cos y x 5 dy y f dx x f df 2 2 2x 2 2 2x x y
2.Atkins – P. 2.22 (Exact differentials) Show that the following functions have exact diffreentials: (a) x2y+3y2, (b) xcos(xy), (c) x3y2, (d) t(t+es)+s Real Gases 3.Atkins P. 1.8 (From last week, virial gas coefficients and compressibility) At 273 K measurements on argon gave B= 21.7 cm3mol-1and C=1200cm6mol-2, where B and C are the second and third virial coefficients in the expansion of Z in powers of 1/Vm. Assuming that the perfect gas law holds sufficiently well for the estimation of the second and third terms of the expansion, calculate the compression factor of argon at 100 atm and 273 K. From your result, estimate the molar volume of argon under these conditions.