The dew point is the temperature at which the air is saturated with moisture and can no longer hold any more water vapor. In other words, it is the temperature at which the air must be cooled in order for water vapor to condense into liquid water.
To calculate the dew point, we need to find the vapor pressure of water at 100% relative humidity and then use this vapor pressure to find the corresponding temperature.
Given:
- Relative humidity = 100%
- Room temperature = 30°C
- Saturated vapor pressure at 30°C = 42400 Pa
Since the relative humidity is 100%, the vapor pressure is equal to the saturated vapor pressure at 30°C:
Vapor Pressure = Saturated vapor pressure = 42400 Pa
Next, we need to find the dew point temperature corresponding to this vapor pressure. We can use the Clausius-Clapeyron equation:
ln(P2/P1) = (L/R)(1/T1 - 1/T2)
where:
P1 = vapor pressure at temperature T1
P2 = vapor pressure at temperature T2
L = latent heat of vaporization of water (2260 kJ/kg)
R = gas constant (8.314 J/(mol*K))
Let's set T1 = 30°C and P1 = 42400 Pa:
ln(42400/P1) = (2260000/8.314)*(1/303 - 1/T2)
Solving for T2 (dew point temperature):
ln(42400/42400) = (2260000/8.314)*(1/303 - 1/T2)
0 = (2260000/8.314)*(1/303 - 1/T2)
1/303 = 1/T2
T2 = 303 K = 30°C
Therefore, the dew point temperature under these conditions is 30°C.
On a particular day, the relative humidity is 100% and the room temperature is o 30 C . What is the dew point? The saturated vapour pressure of water at o 30 C is 42400 Pa.
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