The RMS speed of a gas is 300 m/s. What is the speed of sound in the gas if the
Practice Questions
Q1
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?
300 m/s
400 m/s
500 m/s
600 m/s
Questions & Step-by-Step Solutions
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.
