The highest natural atmospheric temperature ever recorded on Earth was 58°C (136°F), at El Azizia, Libya on September 13, 1922. The record low temperature was −89°C (−129°F), which occurred at the Soviet Vostok Station in Antarctica on July 21, 1983. What is the difference in the speed of sound in air for these two extreme temperatures? answer in m/s.
To calculate the difference in the speed of sound in air for the given extreme temperatures, we need to consider the relationship between temperature and the speed of sound.
The speed of sound in air is directly proportional to the square root of the temperature. The formula to calculate the speed of sound in air is:
v = sqrt(gamma * R * T)
Where:
v is the speed of sound
gamma is the heat capacity ratio
R is the gas constant
T is the temperature in Kelvin
First, let's convert the extreme temperatures into Kelvin:
For the highest temperature:
58°C = 331.15 K
For the lowest temperature:
-89°C = 184.15 K
Now, let's calculate the speed of sound at each temperature using the formula:
For the highest temperature:
v_high = sqrt(gamma * R * T_high)
For the lowest temperature:
v_low = sqrt(gamma * R * T_low)
The heat capacity ratio (gamma) for dry air is approximately 1.4, and the gas constant (R) is around 287 m^2/s^2K.
Plugging in the values and calculating:
For the highest temperature:
v_high = sqrt(1.4 * 287 * 331.15) ≈ 361.94 m/s
For the lowest temperature:
v_low = sqrt(1.4 * 287 * 184.15) ≈ 262.59 m/s
To find the difference, we subtract the lower value from the higher value:
Difference = v_high - v_low ≈ 361.94 m/s - 262.59 m/s ≈ 99.35 m/s
Therefore, the difference in the speed of sound in air for the highest and lowest recorded temperatures is approximately 99.35 m/s.