Answer: (a) Explain why in a gas of N molecules, the

Chapter 18, Problem 18.77

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(a) Explain why in a gas of N molecules, the number of molecules having speeds in the finite interval v to v + v is N = N1 v+v v f 1v2 dv. (b) If v is small, then f 1v2 is approximately constant over the interval and N Nf 1v2v. For oxygen gas 1O2, molar mass 32.0 g>mol2 at T = 300 K, use this approximation to calculate the number of molecules with speeds within v = 20 m>s of vmp. Express your answer as a multiple of N. (c) Repeat part (b) for speeds within v = 20 m>s of 7vmp. (d) Repeat parts (b) and (c) for a temperature of 600 K. (e) Repeat parts (b) and (c) for a temperature of 150 K. (f) What do your results tell you about the shape of the distribution as a function of temperature? Do your conclusions agree with what is shown in Fig. 18.23?