The velocity of sound in an ideal gas can be calculated using the formula:
v = √(γRT)
where: v is the velocity of sound, γ is the adiabatic index (specific heat ratio) of the gas, R is the specific gas constant for the gas, and T is the temperature in Kelvin.
Given: Initial temperature (T1) = 10 degrees Celsius = 10 + 273.15 Kelvin Initial velocity (v1) = 344 m/s
To find the velocity (v2) at a new temperature (T2) of 35 degrees Celsius, we need to convert the temperatures to Kelvin and solve for v2.
T1 = 10 + 273.15 = 283.15 K T2 = 35 + 273.15 = 308.15 K
Using the formula, we can set up a ratio between the initial and final velocities:
v1 / v2 = √(T1 / T2)
Squaring both sides of the equation:
(v1 / v2)^2 = T1 / T2
Rearranging the equation to solve for v2:
v2 = v1 * √(T2 / T1)
Substituting the given values:
v2 = 344 m/s * √(308.15 K / 283.15 K)
Calculating the value:
v2 = 344 m/s * √(1.087)
v2 ≈ 344 m/s * 1.041
v2 ≈ 358.104 m/s
Therefore, the velocity of sound when the temperature changes from 10 degrees Celsius to 35 degrees Celsius is approximately 358.104 m/s.