To determine the speed of sound in air at 0°C, we can use the formula:
v = sqrt(γRT/m)
where:
- v = speed of sound
- γ (gamma) = ratio of heat capacities, which is 1.40
- R = universal gas constant, approximately 8.314 J/(mol·K)
- T = absolute temperature in Kelvin
- m = molar mass in kg/mol
Given:
- Molar mass of air, m = 28.8 x 10-3 kg/mol
- Temperature, T = 0°C = 273.15 K
- γ = 1.40
Now, let’s plug in the values:
R = 8.314 J/(mol·K)
The equation becomes:
v = sqrt(1.40 * 8.314 * 273.15 / (28.8 x 10-3))
Calculating the numerator:
1.40 * 8.314 * 273.15 ≈ 3,488.62677
Now, computing the denominator:
28.8 x 10-3 kg/mol = 0.0288 kg/mol
Therefore:
v = sqrt(3,488.62677 / 0.0288)
Calculating the full equation:
3,488.62677 / 0.0288 ≈ 121,076.1179
v = sqrt(121,076.1179) ≈ 348.5 m/s
So, the speed of sound in air at 0°C is approximately 348.5 meters per second.