Question:
With Laplace correction in Newton’s formula for the velocity of sound in gases, the velocity of sound in monoatomic gas at STP is
With Laplace correction in Newton’s formula for the velocity of sound in gases, the velocity of sound in monoatomic gas at STP is
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For gases:
- Monoatomic: $\gamma = \frac{5}{3}$
- Diatomic: $\gamma = \frac{7}{5}$
Updated On: Apr 30, 2026
- $\sqrt{\frac{7P}{5\rho}}$
- $\sqrt{\frac{5P}{3\rho}}$
- $\sqrt{\frac{2P}{\rho}}$
- $\sqrt{\frac{7P}{2\rho}}$
- $\sqrt{\frac{P}{\rho}}$
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The Correct Option is B
Solution and Explanation
Concept:
With Laplace correction, velocity of sound in gas:
\[
v = \sqrt{\frac{\gamma P}{\rho}}
\]
where $\gamma = \frac{C_P}{C_V}$.
Step 1: Find $\gamma$ for monoatomic gas.
\[ \gamma = \frac{5}{3} \]
Step 2: Substitute in formula.
\[ v = \sqrt{\frac{\gamma P}{\rho}} = \sqrt{\frac{\frac{5}{3}P}{\rho}} \]
Step 3: Simplify.
\[ v = \sqrt{\frac{5P}{3\rho}} \]
Step 1: Find $\gamma$ for monoatomic gas.
\[ \gamma = \frac{5}{3} \]
Step 2: Substitute in formula.
\[ v = \sqrt{\frac{\gamma P}{\rho}} = \sqrt{\frac{\frac{5}{3}P}{\rho}} \]
Step 3: Simplify.
\[ v = \sqrt{\frac{5P}{3\rho}} \]
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