For an assembly of molecules (molar mass =M) at temperature T, the standard deviation of Maxwell's speed is… · ABC26PH0193
Subject: Physical Chemistry · Chapter: Statistical Thermodynamics · Topic: Maxwell Boltzmann · Exam: CSIR NET 2011-2020 · Marks: 2 · Difficulty: Medium
For an assembly of molecules (molar mass $=M$ ) at temperature $T$, the standard deviation of Maxwell's speed is approximately :
(a)$0.7 \sqrt{\frac{R T}{M}}$
(b)$1.4 \sqrt{\frac{R T}{M}}$
(c)$0.7 \sqrt{\left(\frac{M}{R T}\right)}$
(d)$1.4 \sqrt{\frac{M}{R T}}$
Answer
Answer: A ✓ checked by 4AB · confidence high
Explanation
σ = √(⟨v²⟩ − ⟨v⟩²) = √(3RT/M − 8RT/πM) = √(RT/M)·√(3 − 8/π) = 0.67√(RT/M) ≈ 0.7√(RT/M).
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