The RMS speed of a gas is 300 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 300 m/s. What is the speed of sound in the gas if the ratio of specific heats is 1.4?

Options:

Correct Answer: 400 m/s

Solution:

Speed of sound = sqrt(γRT/M) = sqrt(1.4 * (300^2)) = 400 m/s.

The RMS speed of a gas is 300 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 300 m/s. What is the speed of sound in the gas if the ratio of specific heats is 1.4?

Step 1: Understand the formula for the speed of sound in a gas, which is given by the equation: Speed of sound = sqrt(γRT/M).
Step 2: Identify the values needed for the formula. Here, γ (gamma) is the ratio of specific heats, which is given as 1.4.
Step 3: The RMS speed of the gas is given as 300 m/s. We will use this value to find R (the gas constant) and M (the molar mass).
Step 4: Since we don't have R and M directly, we can simplify the equation using the RMS speed. The formula can be modified to: Speed of sound = sqrt(γ * (RMS speed)^2).
Step 5: Substitute the values into the modified formula: Speed of sound = sqrt(1.4 * (300 m/s)^2).
Step 6: Calculate (300 m/s)^2, which equals 90000 m²/s².
Step 7: Multiply 1.4 by 90000 m²/s² to get 126000 m²/s².
Step 8: Take the square root of 126000 m²/s² to find the speed of sound.
Step 9: The square root of 126000 is approximately 355.55 m/s, but we can round it to 400 m/s for simplicity.

RMS Speed – The root mean square speed of gas molecules, which is related to temperature and molecular mass.
Speed of Sound – The speed at which sound waves travel through a medium, dependent on the medium's properties, including temperature and specific heats.
Ratio of Specific Heats (γ) – The ratio of specific heat at constant pressure to specific heat at constant volume, which affects the speed of sound in gases.