On a particular day the relative humidity is 100% and room temperature is 30c. What is the dew point? The saturated vapour pressure of water at 30c is 42400pa
To calculate the dew point, we first need to find the actual vapor pressure at 30°C.
Since the relative humidity is 100%, the actual vapor pressure is equal to the saturated vapor pressure at 30°C, which is 42400 Pa.
Now, we can use the Clausius-Clapeyron equation to find the dew point temperature:
ln(P1/P2) = (-L/R) * (1/T1 - 1/T2)
T1 = initial temperature = 30°C = 303K
P1 = initial pressure = saturated vapor pressure = 42400 Pa
T2 = dew point temperature
P2 = vapor pressure at the dew point = 42400 Pa
R = gas constant = 8.314 J/mol*K
L = latent heat of vaporization of water = 2260 kJ/kg = 2260000 J/kg
Plugging in the values and solving for T2 (dew point temperature):
ln(42400/42400) = (-2260000/8.314) * (1/303 - 1/T2)
0 = (-272251.8) * (0.0033 - 1/T2)
0 = -899.82 - 0.0027/T2
0.0027/T2 = -899.82
T2 = 0.0030 K
Therefore, the dew point temperature at 100% relative humidity and 30°C room temperature is 0.0030 K.