Calculate The Speed Of Sound In Oxygen From The Following Data

Speed of Sound in Oxygen Formula:

\[ v = \sqrt{\frac{\gamma R T}{M}} \]

Adiabatic Index (γ):

unitless

Temperature (T):

Gas Constant (R):

J/mol·K

Molar Mass (M):

kg/mol

Speed of Sound (v):

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1. What is the Speed of Sound in Oxygen?

The speed of sound in oxygen refers to how fast sound waves propagate through oxygen gas. It depends on temperature, pressure, and the properties of the gas. For ideal gases, the speed of sound can be calculated using the adiabatic index, gas constant, temperature, and molar mass.

2. How Does the Calculator Work?

The calculator uses the speed of sound formula for ideal gases:

\[ v = \sqrt{\frac{\gamma R T}{M}} \]

Where:

\( v \) — Speed of sound (m/s)
\( \gamma \) — Adiabatic index (unitless)
\( R \) — Gas constant (8.314 J/mol·K)
\( T \) — Temperature (K)
\( M \) — Molar mass (0.032 kg/mol for oxygen)

Explanation: The formula shows that the speed of sound increases with temperature and decreases with molar mass. For oxygen, the adiabatic index (γ) is approximately 1.4.

3. Importance of Speed of Sound Calculation

Details: Calculating the speed of sound in oxygen is important in various scientific and engineering applications, including aerodynamics, acoustics, meteorology, and the design of pneumatic systems.

4. Using the Calculator

Tips: Enter the adiabatic index (typically 1.4 for diatomic gases like oxygen), temperature in Kelvin, and gas constant (default is 8.314 J/mol·K). The molar mass is fixed at 0.032 kg/mol for oxygen.

5. Frequently Asked Questions (FAQ)

Q1: What is the typical value of γ for oxygen?
A: For diatomic gases like oxygen, the adiabatic index (γ) is approximately 1.4.

Q2: How does temperature affect the speed of sound?
A: The speed of sound increases with temperature, as shown by the direct relationship in the formula.

Q3: Why is molar mass important in this calculation?
A: Heavier molecules move more slowly, resulting in a lower speed of sound. Lighter gases generally have higher sound speeds.

Q4: Does pressure affect the speed of sound in gases?
A: For ideal gases at constant temperature, pressure has no effect on the speed of sound, as it cancels out in the derivation.

Q5: How accurate is this calculation for real oxygen gas?
A: This formula provides a good approximation for ideal gases. For more precise calculations at high pressures or extreme temperatures, more complex equations of state may be needed.