Outdoors, the air temperature is 5 °C (44 °F) and the relative humidity is 45%. What is the relative humidity of the air if it is drawn indoors and heated to 20 °C (68 °F)? Assume that no water vapor is added to or removed from the air. Answer: _______% (Round to nearest whole number, do not include units.)
45%
To find the relative humidity indoors after heating the air, we can use the concept of dew point temperature.
The dew point temperature is the temperature at which the air becomes saturated and water vapor starts to condense. If the air temperature decreases below the dew point temperature, the excess moisture in the air will begin to condense as dew or fog.
First, we need to find the dew point temperature outdoors. We can use a dew point calculator or formula to calculate it.
Assuming the air pressure is constant, one formula for estimating the dew point temperature is:
Td = T - ((100 - RH) / 5)
Where Td is the dew point temperature in °C, T is the temperature in °C (5 °C in this case), and RH is the relative humidity (45% in this case).
Plugging in the values, we get:
Td = 5 - ((100 - 45) / 5)
Td = 5 - (55 / 5)
Td = 5 - 11
Td = -6 °C
Now, we can find the new relative humidity indoors after heating the air.
Using the same formula, but now using the new temperature indoors (20 °C) and the calculated dew point temperature outdoors (-6 °C), we get:
RH_indoors = 100 - (5 × (20 - (-6)))
RH_indoors = 100 - (5 × 26)
RH_indoors = 100 - 130
RH_indoors = -30%
However, negative relative humidity values are not possible, as it indicates a physically impossible scenario. This means that the air indoors is not saturated and no condensation will occur.
Therefore, the relative humidity will remain at 45% indoors when heated to 20 °C.
To determine the relative humidity of the air when it is drawn indoors and heated to 20 °C (68 °F), we can use the concept of relative humidity remaining constant when the amount of water vapor in the air does not change.
Given:
- Outdoor air temperature = 5 °C (44 °F)
- Outdoor relative humidity = 45%
- Indoor air temperature = 20 °C (68 °F)
First, we need to calculate the saturation vapor pressure at both temperatures using the Antoine equation. The Antoine equation is a mathematical expression that relates the vapor pressure of a substance to its temperature. For water, it is given by:
log (P) = A - B / (T + C)
Where:
- P is the saturation vapor pressure in mmHg
- T is the temperature in °C
- A, B, and C are constants specific to the substance
For water, the constants are:
- A = 8.07131
- B = 1730.63
- C = 233.426
Using the Antoine equation, we can calculate the saturation vapor pressure at each temperature:
For 5 °C:
P1 = 10^(A - B / (T1 + C))
P1 = 10^(8.07131 - 1730.63 / (5 + 233.426))
P1 = 5.55 mmHg
For 20 °C:
P2 = 10^(A - B / (T2 + C))
P2 = 10^(8.07131 - 1730.63 / (20 + 233.426))
P2 = 17.54 mmHg
Now, we can use the definition of relative humidity, which is the ratio of the actual vapor pressure to the saturation vapor pressure at a given temperature. Let's denote the relative humidity as RH.
For the outdoor air at 5 °C:
RH1 = (actual vapor pressure1 / saturation vapor pressure1) * 100
RH1 = (45 / 100) * 100
RH1 = 45%
Since the relative humidity remains constant when the amount of water vapor does not change, we can assume that the indoor air at 20 °C will have the same relative humidity.
Therefore, the answer is 45%.
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Sra