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Zorluk: ZorVapour Pressure, Boiling, Evaporation, and Relative Humidity

If a sample of unsaturated air with a relative humidity of 40%40\% at 30∘C30^\circ\text{C} is compressed isothermally to one-third of its original volume, the final relative humidity of the air will be 100%100\%.

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True. The relative humidity cannot exceed 100% because water vapour condenses into liquid once its partial pressure reaches the saturated vapour pressure at that temperature.
The statement is true because relative humidity is the ratio of actual partial vapour pressure to saturated vapour pressure at a specific temperature. Although isothermal compression to one-third volume triples the partial pressure of water vapour (giving a theoretical 120%), partial vapour pressure is bounded by the saturated vapour pressure. When the relative humidity reaches 100%, condensation occurs, keeping the relative humidity at exactly 100%.

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1
Apply Boyle's law to calculate the theoretical partial vapour pressure after isothermal compression.
Since volume is reduced to 13V1\frac{1}{3}V_1 at constant temperature, the partial pressure of water vapour would increase by a factor of 3 (p2=3p1p_2 = 3p_1).
For an unsaturated vapour at constant temperature, partial pressure is inversely proportional to volume.
2
Determine the theoretical relative humidity from the pressure ratio.
\text{Theoretical R.H.} = 3 \times 40\% = 120\%.
Relative humidity is defined as R.H.=pps×100%\text{R.H.} = \frac{p}{p_s} \times 100\%, where pp is the partial pressure and psp_s is the saturated vapour pressure.
3
Apply the physical limit imposed by saturated vapour pressure.
The actual relative humidity cannot exceed 100%100\%; excess vapour condenses.
Saturated vapour pressure psp_s represents the maximum possible partial pressure of water vapour in air at a given temperature.

Anahtar Kavram

Saturated Vapour Pressure Limit and Relative Humidity under Isothermal Compression
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Konular

Vapour Pressure, Boiling, Evaporation, and Relative Humidity

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