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GATE 2021 ME (ME1) – Question 25

Thermal Engineering Applications · Psychrometry and air-conditioning · 1 mark · Multiple choice

The relative humidity of ambient air at 300 K is 50% with a partial pressure of water vapour equal to $p_v$. The saturation pressure of water at 300 K is $p_{sat}$. The correct relation for the air-water mixture is

  1. $p_v=0.5p_{sat}$
  2. $p_v=p_{sat}$
  3. $p_v=0.622p_{sat}$
  4. $p_v=2p_{sat}$

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Show answer and explanation

Correct answer: (A) $p_v=0.5p_{sat}$

Explanation

Relative humidity is $\phi=p_v/p_{sat}$ at the same temperature. Substituting φ=0.5 gives **pᵥ=0.5 pₛₐₜ (A)**.

The factor 0.622 belongs to the humidity-ratio formula and is not relative humidity.