Answer:
To determine the relative humidity, we need to compare the actual vapor pressure of the air to the saturation vapor pressure at the given temperature. The saturation vapor pressure can be calculated using the Magnus formula:
Saturation Vapor Pressure (SVP) = 6.11 * 10^((7.5 * T) / (T + 237.3))
where T is the temperature in degrees Celsius.
In this case, the travel temperature is 4°C, so we can calculate the saturation vapor pressure at that temperature:
SVP = 6.11 * 10^((7.5 * 4) / (4 + 237.3))
= 6.11 * 10^(30 / 241.3)
= 6.11 * 10^0.124
SVP ≈ 6.11 * 1.32
SVP ≈ 8.07 hPa
Now let's calculate the actual vapor pressure using the dew point temperature. The actual vapor pressure is the pressure exerted by water vapor in the air at a given temperature:
Actual Vapor Pressure = 6.11 * 10^((7.5 * DP) / (DP + 237.3))
where DP is the dew point temperature in degrees Celsius.
In this case, the dew point temperature is -4°C, so we can calculate the actual vapor pressure at that temperature:
Actual Vapor Pressure = 6.11 * 10^((7.5 * -4) / (-4 + 237.3))
= 6.11 * 10^(-30 / 233.3)
= 6.11 * 10^(-0.128)
Actual Vapor Pressure ≈ 6.11 * 0.75
Actual Vapor Pressure ≈ 4.58 hPa
Finally, we can calculate the relative humidity using the following formula:
Relative Humidity = (Actual Vapor Pressure / Saturation Vapor Pressure) * 100
Relative Humidity = (4.58 / 8.07) * 100
Relative Humidity ≈ 56.7%
Therefore, if the temperature is 4°C and the dew point is -4°C, the relative humidity of the air is approximately 56.7%.
Step-by-step explanation: