The RMS speed of a gas is 400 m/s. What is the speed of sound in the gas if the

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Question: The RMS speed of a gas is 400 m/s. What is the speed of sound in the gas if the ratio of specific heats is 1.4?

Options:

Correct Answer: 560 m/s

Solution:

The speed of sound in a gas is given by c = sqrt(γRT/M). For an ideal gas, c is approximately 1.4 times the RMS speed.

The RMS speed of a gas is 400 m/s. What is the speed of sound in the gas if the ratio of specific heats is 1.4?

The RMS speed of a gas is 400 m/s. What is the speed of sound in the gas if the ratio of specific heats is 1.4?

Step 1: Understand that the RMS speed of a gas is given as 400 m/s.
Step 2: Know that the ratio of specific heats (γ) is given as 1.4.
Step 3: Recall the relationship between the speed of sound (c) in a gas and the RMS speed (v_rms). For an ideal gas, c is approximately 1.4 times the RMS speed.
Step 4: Calculate the speed of sound using the formula: c = 1.4 * v_rms.
Step 5: Substitute the value of v_rms: c = 1.4 * 400 m/s.
Step 6: Perform the multiplication: c = 560 m/s.
Step 7: Conclude that the speed of sound in the gas is 560 m/s.

RMS Speed – The root mean square speed of gas molecules, which is a measure of the average speed of particles in a gas.
Speed of Sound – The speed at which sound waves propagate through a medium, which depends on the medium's properties, including temperature and specific heats.
Ratio of Specific Heats (γ) – The ratio of the specific heat at constant pressure to the specific heat at constant volume, which influences the speed of sound in a gas.
Ideal Gas Law – A fundamental equation that relates pressure, volume, temperature, and the number of moles of a gas, often used in thermodynamic calculations.