On a warm summer day in Athens, the temperature is 33C (dry bulb temperature) and the relative humidity is 60%. What is the absolute humidity? (kg/kg Dry air)
What is the humid volume of the air? (m^3 / kg Dry Air)
What is the specific enthalpy of the air, taking H2O (L, 0C, 1atm) as a reference state? (kJ/ kg Dry air)
What is the web bulb temperature? (C)
What is the dew point temperature? (C)
To answer these questions, we need to use some psychrometric properties and calculations. Psychrometry is the study of the physical and thermodynamic properties of gas-vapor mixtures, such as air and water vapor.
1. Absolute Humidity (kg/kg Dry air):
Absolute humidity is the mass of water vapor in a given volume of air, expressed as kilograms of water vapor per kilogram of dry air.
To calculate absolute humidity, you need to know the vapor pressure and the atmospheric pressure. However, since we only know the relative humidity and dry bulb temperature, we need to make some assumptions and approximations.
Relative Humidity (RH) is defined as the ratio of the partial pressure of water vapor to the saturation pressure at the same temperature. We can estimate the saturation pressure using the Antoine equation which provides a relationship between temperature and saturation pressure.
P_sat = 10^(A - (B / (T + C))), where T is the temperature in degrees Celsius.
Using the values A = 8.07131, B = 1730.63, and C = 233.426, we can find the saturation pressure at 33C.
P_sat = 10^(8.07131 - (1730.63 / (33 + 233.426)))
P_sat = 4.0717 kPa
To find the partial pressure of water vapor, we multiply the saturation pressure by the relative humidity (RH) expressed as a decimal.
Partial Pressure of water vapor = RH * P_sat
Partial Pressure of water vapor = 0.60 * 4.0717 kPa
Partial Pressure of water vapor = 2.443 kPa
Now, to find the absolute humidity, we need to convert the partial pressure of water vapor to kilograms of water vapor per kilogram of dry air. For this, we can use the ideal gas law and the molar mass of water vapor (Mw = 18.01528 g/mol). The ideal gas law states that PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the gas constant, and T is the temperature.
Partial pressure of water vapor = n_water_vapor * R_specific * T, where R_specific is the specific gas constant for water vapor (461.52 J/(kg·K))
Converting the units:
Partial pressure of water vapor = n_water_vapor * R_specific * T * (1 kPa / 1000 Pa)
Partial pressure of water vapor = n_water_vapor * R_specific * T * 0.001
Since n_water_vapor is the number of moles, we can find the mass of water vapor as:
Mass of water vapor = n_water_vapor * Mw
Now, equating the two expressions:
Mass of water vapor * R_specific * T * 0.001 = Partial pressure of water vapor
Solving for Mass of water vapor:
Mass of water vapor = (Partial pressure of water vapor) / (R_specific * T * 0.001)
Substituting the known values:
Mass of water vapor = (2.443 kPa) / (461.52 J/(kg·K) * (33 + 273.15) K * 0.001)
Finally, dividing the Mass of water vapor by the mass of dry air gives us the absolute humidity:
Absolute Humidity = Mass of water vapor / Mass of dry air
2. Humid Volume (m^3/kg Dry Air):
The humid volume is the volume of the mixture of dry air and water vapor per unit mass of dry air.
To calculate the humid volume, we need to use the ideal gas law again.
Humid Volume = R_specific * (T + 273.15) / P
Substituting the known values:
Humid Volume = 461.52 J/(kg·K) * (33 + 273.15) K / (101.325 kPa)
3. Specific Enthalpy (kJ/ kg Dry air):
Specific enthalpy is the amount of energy added to or removed from the air per unit mass of dry air.
To calculate the specific enthalpy, we need to use the psychrometric chart or specific enthalpy tables. Unfortunately, we cannot calculate this directly given the provided information.
4. Wet Bulb Temperature (C):
The wet bulb temperature is the temperature of a parcel of air when cooled by the process of evaporating water into it.
To calculate the wet bulb temperature, we need additional information such as the wet bulb depression or use a psychrometric chart.
5. Dew Point Temperature (C):
The dew point temperature is the temperature at which the air becomes saturated and condensation occurs.
To calculate the dew point temperature, we need to use the wet bulb temperature and the difference between dry bulb temperature and wet bulb temperature. We also need to know the psychrometric properties or use a dew point calculator that considers relative humidity.
In summary, we can calculate the absolute humidity, humid volume, wet bulb temperature, and dew point temperature based on the provided dry bulb temperature, relative humidity, and using additional information from psychrometric properties, equations, or tables. However, the specific enthalpy cannot be calculated with the given information alone.