Compute the relative humidity (RH) to nearest percent for each of the following atmospheric conditions: (Round to one decimal place, do not include units.)
a. mixing ratio = 2.3 g/kg, temperature = 10 °C (50 °F), RH = _________ %
To compute the relative humidity (RH) for a given mixing ratio and temperature, we can use the concept of saturation mixing ratio and the formula for relative humidity.
1. First, we need to calculate the saturation mixing ratio (Ws) at the given temperature.
- The saturation mixing ratio represents the maximum amount of moisture the air can hold before it becomes saturated.
- We can calculate it using empirical formulas or lookup tables specifically designed for this purpose.
- For simplicity, let's use the formula Ws = 6.11 * 10^((7.5*T)/(237.7+T)), where T is the temperature in degrees Celsius.
For our given temperature of 10 °C, we have:
Ws = 6.11 * 10^((7.5*10)/(237.7+10))
2. Next, we can calculate the actual mixing ratio (W) using the given value of 2.3 g/kg.
3. Now, we can compute the relative humidity (RH) using the following formula:
RH = (W / Ws) * 100
For our given values of W = 2.3 g/kg and Ws from step 1, we have:
RH = (2.3 / Ws) * 100
To round the answer to the nearest percent, perform the final calculation and round the result to the nearest whole number.
Note: If the temperature was given in Fahrenheit, we would need to convert it to Celsius before proceeding with the calculations.
To convert Fahrenheit to Celsius, use the formula C = (F - 32) * (5/9).
So, with the steps outlined above, you can now calculate the relative humidity (RH) to the nearest percent for the given atmospheric conditions.