On a clear and calm day, the air temperature at sunrise is 5 °C (41 °F) with a relative humidity of 90%. The air temperature reaches a maximum of 15 °C (59 °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.)

Well, when it comes to predicting the value of relative humidity, I like to turn into a weather joker. So, here's a little weather humor for you!

Why did the cloud go to therapy?

Because it had low self-esteem and felt a little too down-to-earth!

Now, onto your question. To predict the relative humidity at 3 p.m., we need to analyze the temperature change throughout the day. From 5 °C (41 °F) to 15 °C (59 °F), we see a rise of 10 °C (18 °F).

Now, here's a funny twist. The relative humidity of 90% at sunrise was high, but as the temperature increases during the day, the air has the potential to hold more moisture. So, the relative humidity is likely to decrease by the afternoon.

While I can't give an exact number without more data, we can assume that the relative humidity will decrease a bit. So, let's play it safe and say that the approximate value of relative humidity at 3 p.m. could be around 80%.

Keep in mind that this is just a funny prediction. Actual weather conditions may vary!

To predict the value of the relative humidity at 3 p.m., we need to consider the relationship between temperature and relative humidity.

Relative humidity is a measure of the amount of moisture in the air compared to the maximum amount of moisture the air can hold at a given temperature. Warmer air is capable of holding more moisture than colder air before it becomes saturated.

In this case, the air temperature increases from 5 °C at sunrise to 15 °C at 3 p.m., and no water vapor is added or removed from the air. We can assume that the amount of moisture in the air remains constant throughout the day.

To determine the relative humidity at 3 p.m., we need to compare the maximum amount of moisture the air can hold at 15 °C to the actual amount of moisture in the air.

We can use the concept of saturation vapor pressure to calculate this. Saturation vapor pressure represents the maximum amount of water vapor the air can hold at a given temperature. It increases with temperature.

First, we can calculate the saturation vapor pressure at sunrise, when the temperature is 5 °C. There are different equations to calculate this, but one commonly used formula is the Magnus formula:

Es = 6.11 * 10^(7.5*T / (T + 237.3))

where Es is the saturation vapor pressure in Pascal and T is the temperature in Celsius.

Using this formula, we find that at 5 °C, the saturation vapor pressure is approximately 872 Pa.

Next, we calculate the saturation vapor pressure at 15 °C:

Es = 6.11 * 10^(7.5*(15) / (15 + 237.3))

This gives us a saturation vapor pressure of approximately 1817 Pa.

Now, we can calculate the actual vapor pressure at 3 p.m. using the saturation vapor pressure at 15 °C and the relative humidity at sunrise.

Since relative humidity is the ratio of the actual vapor pressure to the saturation vapor pressure (expressed as a percentage), we can rearrange the equation to solve for the actual vapor pressure:

Actual Vapor Pressure = Relative Humidity * Saturation Vapor Pressure / 100

Using the given relative humidity of 90% and the saturation vapor pressure at 15 °C of 1817 Pa, we can calculate the actual vapor pressure:

Actual Vapor Pressure = 90 * 1817 / 100 = 1635.3 Pa

Finally, to find the relative humidity at 3 p.m., we compare the actual vapor pressure (1635.3 Pa) to the saturation vapor pressure at 15 °C (1817 Pa).

Relative Humidity = Actual Vapor Pressure / Saturation Vapor Pressure * 100

Relative Humidity = 1635.3 / 1817 * 100 ≈ 89.9 ≈ 90%

Therefore, the predicted value of the relative humidity at 3 p.m. is 90%.