To calculate the specific conditions required to achieve a specific relative humidity with a given air temperature and volume, we need to consider the relationship between temperature, relative humidity, and the saturation point of the air.
Relative humidity is a measure of the amount of moisture present in the air compared to the maximum amount of moisture the air can hold at a given temperature. The saturation point is the point at which the air is holding the maximum amount of moisture it can at a particular temperature.
Here's a general process to determine the specific conditions:
Convert the air temperature to Kelvin: T = 50°C + 273.15 = 323.15 K
Determine the saturation vapor pressure at the given temperature using the Antoine equation or other relevant vapor pressure data. Let's assume the saturation vapor pressure is 1 atmosphere (atm) for simplicity.
Calculate the vapor pressure at the desired relative humidity. Relative humidity (RH) is expressed as a percentage. To convert it to a decimal, divide by 100. RH = 0.9
Vapor Pressure = RH * Saturation Vapor Pressure = 0.9 * 1 atm = 0.9 atm
Use the ideal gas law to calculate the amount of water vapor in moles: PV = nRT
Given: P = Vapor Pressure = 0.9 atm V = Volume = 25 cubic meters R = Gas constant = 0.0821 atm·m³/(mol·K) T = Temperature = 323.15 K
n = (PV) / (RT) = (0.9 atm * 25 m³) / (0.0821 atm·m³/(mol·K) * 323.15 K)
This will give you the number of moles of water vapor present in the given volume.
Convert the moles of water vapor to kilograms: Multiply the number of moles by the molar mass of water (18.01528 g/mol) and convert to kilograms.
Finally, you will have the mass of water vapor in kilograms in the given volume to achieve a relative humidity of 90% at 50°C.
Please note that this calculation assumes ideal gas behavior and doesn't consider other factors that may affect humidity, such as other gases present or non-ideal conditions. It is always advisable to consult relevant humidity charts, tables, or use specialized instruments to accurately measure and control humidity in practical scenarios.