Question

Difficulty: HardVapour Pressure, Boiling, Evaporation, and Relative Humidity

When air containing unsaturated water vapour is cooled at constant atmospheric pressure without adding or removing moisture, the saturated vapour pressure of water decreases while the actual partial vapour pressure of water remains constant until the dew point is reached.

Answer: Answer

Answer

True. Saturated vapour pressure decreases as temperature falls, while actual partial vapour pressure remains constant under constant total pressure until condensation starts at the dew point.
The statement is correct because saturated vapour pressure is a temperature-dependent property that decreases as air cools. So long as total pressure remains unchanged and no water vapour is added or removed, the actual partial vapour pressure of the water vapour stays constant until the dew point is reached, at which point the air becomes saturated (100%100\% relative humidity) and condensation begins.

Step-by-Step Solution

1
Analyze the temperature dependence of saturated vapour pressure (SVP).
SVP decreases as temperature drops.
SVP is determined by the kinetic energy of water molecules escaping into vapour at dynamic equilibrium, which decreases with decreasing temperature.
2
Determine the behavior of the actual partial vapour pressure of water during cooling at constant total pressure.
Actual partial vapour pressure remains constant prior to condensation.
Dalton's law dictates that partial pressure depends on the mole fraction of water vapour and total pressure; since no water vapour is added or removed, actual partial vapour pressure does not change.
3
Evaluate the condition for reaching the dew point.
At the dew point, SVP drops to equal the constant actual partial vapour pressure, achieving 100% relative humidity.
Relative humidity is defined as R.H.=PactualPSVP×100%\text{R.H.} = \frac{P_{\text{actual}}}{P_{\text{SVP}}} \times 100\%; as PSVPP_{\text{SVP}} decreases towards PactualP_{\text{actual}}, R.H.\text{R.H.} increases to 100%100\%.

Key Concept

Saturated vs. actual vapour pressure, temperature dependence of SVP, and dew point
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