Physics · Kinetic Theory of Gases

JEE Main 2024 — 31 January, Shift 2 — Question 35

The speed of sound in oxygen at S.T.P. will be approximately: (Given, R=8.3JK−1,γ=1.4\mathrm{R}=8.3 \mathrm{JK}^{-1}, \gamma=1.4 )

  1. Option A:

    315 m/s315 \mathrm{~m} / \mathrm{s}

    Correct
  2. Option B:

    333 m/s333 \mathrm{~m} / \mathrm{s}

  3. Option C:

    341 m/s341 \mathrm{~m} / \mathrm{s}

  4. Option D:

    325 m/s325 \mathrm{~m} / \mathrm{s}

Answer: A

Step-by-step solution

\text{Given:} \quad &R = 8.3 \text{ J K}^{-1} \text{ mol}^{-1} \\ &\gamma = 1.4 \\ &\text{STP conditions: } T = 273.15 \text{ K}, \, P = 1 \text{ atm} = 1.01325 \times 10^5 \text{ Pa} \\ &\text{Molar mass of O}_2: \, M = 32 \times 10^{-3} \text{ kg mol}^{-1} \end{aligned}$$ $$\begin{aligned} \text{Formula for speed of sound:} \quad v = \sqrt{\frac{\gamma RT}{M}} \end{aligned}$$ $$\begin{aligned} \text{Substituting values:} \quad v &= \sqrt{\frac{1.4 \times 8.3 \times 273.15}{32 \times 10^{-3}}} \\ &= \sqrt{\frac{3174.537}{0.032}} \\ &= \sqrt{99204.28} \\ &= 314.97 \text{ m/s} \\ &\approx 315 \text{ m/s} \end{aligned}$$ $$\begin{aligned} \boxed{v = 315 \text{ m/s}} \end{aligned}$$

Answer key and solution verified before publishing.

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Exam
JEE Main 2024
Subject
Physics
Chapter
Kinetic Theory of Gases
Topic
Pressure of Gas and Different speeds of Gas Molecules
The speed of sound in oxygen at S.T.P. will be approximately: (Given… | JEE Main 2024 PYQ with Solution · DhiX AI