Subtopic: Psychrometry – properties of air-water vapour mixture
Question Statement:
Specific heat capacity of dry air and water vapour are 1.005 and 1.88 kJ kg⁻¹K⁻¹, respectively. In an energy conserving system, 1 kg s⁻¹ air at 30°C with constant absolute humidity of 0.02 kg water (kg dry air)⁻¹ is heated up to 65ºC. Water at the wet bulb temperature of air is then sprayed into the air so that the final temperature of the air-water vapour mixture is 40ºC. Latent heat of vapourization of water at 70°C and 40°C are 2334 and 2407 kJ kg⁻¹, respectively. The absolute humidity of the exhaust air from the spray chamber in kg water (kg dry air)⁻¹is
Options:
(A) 0.027
(B) 0.029
(C) 0.031
(D) 0.033
Official Answer Key:
C
Step-by-Step Solution & Explanation
In the spray chamber, sensible heat lost by the air (cooling from 65°C to 40°C) equals the latent heat absorbed by the evaporating spray water (using the latent heat at the 40°C exit condition):
ΔW×L_v(40°C) = C_s×(65−40) ⇒ ΔW = 1.0426×25/2407 = 0.01083 kg water/kg dry air.
Exit absolute humidity, W₂ = W₁+ΔW = 0.02+0.01083 = 0.0308 ≈ 0.031. Answer: (C).
Section 7 — Dairy and Food Engineering
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