On a clear and calm day, the air temperature at sunrise is 0 °C (32 °F) with a relative humidity of 85%. The air temperature reaches a maximum of 10 °C (50 °F) at 3 p.m. Assuming that no water vapor is added to or removed from the air, predict the value of the relative humidity at 3 p.m. Answer: _____ % (Round to the nearest whole number, do not include units.)
Here are the answers to the whole math section of that Meteorology test. (i took it and got them all right)
I took the test from a Meteorology class so here's the correct answers:
1.) 100%
2.) a. 25%
b. 33%
c. 100%
3.) 17%
4.) a. 24mb
b. 20
5.) 42%
To predict the value of the relative humidity at 3 p.m., we can use the concept of the dew point temperature. The dew point temperature is the temperature at which the air becomes saturated and condensation begins to form. It is a measure of how much moisture is present in the air.
Given the air temperature at sunrise is 0 °C (32 °F) and the relative humidity is 85%, we can determine the dew point temperature using weather data or a dew point calculator. For simplicity, let's assume the dew point temperature is also 0 °C (32 °F) at sunrise.
To find the relative humidity at 3 p.m., we need to compare the air temperature at that time with the dew point temperature. If the air temperature is below the dew point, the air is not saturated, and the relative humidity will be less than 100%. If the air temperature is equal to the dew point, the air is saturated, and the relative humidity will be 100%. If the air temperature is higher than the dew point, the air is unsaturated, and the relative humidity will be less than 100%.
In this case, the air temperature at 3 p.m. is 10 °C (50 °F). Since 10 °C (50 °F) is higher than the assumed dew point temperature of 0 °C (32 °F), we conclude that the air is unsaturated.
To predict the value of the relative humidity, we need to consider the relation between the actual vapor pressure (e) and the saturation vapor pressure (es) at the given temperature. Relative humidity (RH) is calculated as (e / es) × 100%.
To calculate the saturation vapor pressure at 10 °C (50 °F), we can use the Magnus formula:
es = 6.11 * 10^[(7.5 * T) / (237 + T)]
Where T is the temperature in degrees Celsius.
Plugging in T = 10 °C, we get:
es = 6.11 * 10^[(7.5 * 10) / (237 + 10)]
es = 12.29
So, the saturation vapor pressure at 10 °C is 12.29 mmHg.
Since we know the air is unsaturated, the actual vapor pressure will be less than the saturation vapor pressure. Let's assume the actual vapor pressure at 10 °C is 9 mmHg (you can obtain this value from weather data or using instruments like a hygrometer).
Using the formula for relative humidity:
RH = (e / es) × 100%
RH = (9 / 12.29) × 100%
RH ≈ 73.31%
Therefore, the predicted value of the relative humidity at 3 p.m. is approximately 73%.