The speed of sound in air varies with temperature. The general equation that relates the speed of sound to temperature is:
v = √(γ * R * T)
Where:
- v is the speed of sound
- γ is the adiabatic index (approximately 1.4 for air)
- R is the gas constant for air (approximately 287.1 J/(kg·K))
- T is the temperature in Kelvin
To convert Celsius to Kelvin, you need to add 273.15 to the Celsius temperature. So, to find the speed of sound at 100°C, we need to convert it to Kelvin:
T = 100°C + 273.15 = 373.15 K
Now, we can calculate the speed of sound at 100°C:
v = √(1.4 * 287.1 J/(kg·K) * 373.15 K) ≈ 349.02 m/s
Therefore, at a temperature of 100°C, the speed of sound in air is approximately 349.02 meters per second.