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

QUESTION:

CALC (a) Explain why in a gas of \(N\) molecules, the number of molecules having speeds in the finite interval \(v\) to \(v+\Delta v\) is \(\Delta N=N \int_{v}^{v+\Delta v} f(v) d v\). (b) If \(\Delta v\) is small, then \(f(v)\) is approximately constant over the interval and \(\Delta N \approx N f(v) \Delta v\). For oxygen gas ( \(\mathrm{O}_{2}\), molar mass 32 \(\mathrm{gm} / \mathrm{mol}\) at \(T=300 \mathrm{~K}\), use this approximation to calculate the number of molecules with speeds within \(\Delta v=20 \mathrm{~m} / \mathrm{s}\) of \(v_{m p}). Express your answer as a multiple of  (c) Repeat part (b) for speeds within \(\Delta v=20 \mathrm{~m} / \mathrm{s}\) of \(7 v_{m p}\) (d) Repeat parts (b) and (c) for a temperature of . (e) Repeat parts (b) and (c) for a temperature of . (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.  ?

Equation Transcription:

Text Transcription:

N

v

v+ delta v

delta N=N integral _v^v+v f (v)dv

delta v

f(v)

delta N approx N f(v) delta v

O_2

T=300 K

delta v=20 m/s

v_mp

delta v=20 m/s

7 v_mp

gm/mol

deltav=20 m/s

v_mp