Chemistry - Ideal Gas Question with Solution | TestHub
ChemistryIdeal GasMaxwell's Distribution LawMedium2 minQB
ChemistryMediumsingle choice
Passage / Comprehension
According to Maxwell's distribution law, the fraction of molecules per unit change in speed [velocity distribution function, f(c)], traveling with the speed from C to C + dC is given as:
f(c) = (1/dC)·(dN/N) = 4π·(M / 2πRT)3/2·C2·e(-MC2/2RT). (R = 8.0 J/K-mol, ln 2 = 0.7)
At what speed of the molecules, the value of the Maxwell distribution function f(c) for the temperature T will be the same as that of the temperature n times higher?
Options:
Answer:
B
Solution:
Set f(c, T) = f(c, nT): T-3/2e-Mc2/2RT = (nT)-3/2e-Mc2/2RnT. Taking logs, 3/2ln n = (Mc2)/(2RT)(1 - 1/n) = (Mc2(n-1))/(2RTn). Hence c2 = (3RT,nln n)/(M(n-1)), so c = √(3RT,nln n/M(n-1)). Hence Ans (b).
Stream:JEESubject:ChemistryTopic:Ideal GasSubtopic:Maxwell's Distribution Law
⏱ 2mℹ️ Source: QB
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