What is the ratio of the speed of sound in air at 0°C to the speed at 100°C?
Ratio = (331+0.6T1)/(331+0.6T2) =
(331+0)/(331+60) = 0.847
To find the ratio of the speed of sound in air at 0°C to the speed at 100°C, we need to consider the relationship between temperature and the speed of sound in air.
The speed of sound in air is directly proportional to the square root of the absolute temperature. The formula to calculate the speed of sound is given by:
v = √(γRT)
Where:
v = speed of sound
γ = adiabatic index (for air it is approximately 1.4)
R = specific gas constant (for air it is approximately 287 J/(kg·K))
T = absolute temperature in kelvin (0°C = 273K, 100°C = 373K)
To find the ratio, we can substitute the temperatures into the formula and take the ratio:
v0 = √(γR273)
v100 = √(γR373)
Ratio = v0 / v100 = (√(γR273)) / (√(γR373))
Calculating the values:
γ = 1.4
R = 287 J/(kg·K)
273 K = 273
373 K = 373
Substituting the values into the equation:
v0 / v100 = (√(1.4 × 287 × 273)) / (√(1.4 × 287 × 373))
After plugging in the values and calculating the numerator and denominator separately, we can divide to find the ratio. The actual numerical value of this ratio will be dependent on the specific values of γ and R used for the calculation.
To find the ratio of the speed of sound in air at 0°C to the speed at 100°C, we need to first determine the formula that relates the speed of sound in air to temperature. The speed of sound in air is given by:
v = √(γ * R * T)
where:
v = speed of sound
γ = adiabatic index of air
R = specific gas constant for air
T = temperature in Kelvin
The adiabatic index, γ, is approximately 1.4 for dry air, and the specific gas constant, R, is approximately 287 J/(kg*K) for air.
Now, let's calculate the speed of sound at 0°C and 100°C separately.
At 0°C:
T₀ = 0 + 273.15 = 273.15 K
v₀ = √(γ * R * T₀)
At 100°C:
T₁ = 100 + 273.15 = 373.15 K
v₁ = √(γ * R * T₁)
Finally, we can find the ratio by dividing the speed at 0°C by the speed at 100°C:
Ratio = v₀ / v₁
Now you can substitute the values for γ, R, T₀, and T₁ into the equations above, calculate the values for v₀ and v₁, and divide them to find the ratio.