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, )
- Option A:Correct
- Option B:
- Option C:
- Option D:
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
- Paper
- 31 January, Shift 2
- Subject
- Physics
- Chapter
- Kinetic Theory of Gases
- Topic
- Pressure of Gas and Different speeds of Gas Molecules