The humidity ratio of atmospheric air at 28°C [] dry bulb temperature and 760 mm Hg pressure is 0.018 kg/kg of dry air. What will be the relative humidity of air?

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  1. 96.13%
  2. 75.42%
  3. 55.25%
  4. 88.35%

Answer (Detailed Solution Below)

Option 2 : 75.42%
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Concept:

Relative humidity is given by:

\( \phi = \frac{P_v}{P_{sat}} \times 100 \)

Where partial vapor pressure is calculated using:

\( P_v = \frac{\omega \times P}{0.622~ + ~\omega} \)

Given:

  • \( \omega = 0.018 \)
  • \( P = 760 \, \text{mm Hg} \)
  • \( P_{sat} = 28.34 \, \text{mm Hg} \)

Calculation:

\( P_v = \frac{0.018 \times 760}{0.622 + 0.018} \approx 21.375 \, \text{mm Hg} \)

\( \phi = \frac{21.375}{28.34} \times 100 \approx {75.42\%} \)

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