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 thermal energy supplied per second during heating in kW is
Options:
(A) 18.2
(B) 36.5
(C) 101.0
(D) 166.8
Official Answer Key:
B
Step-by-Step Solution & Explanation
Humid specific heat of the air-water vapour mixture, C_s = C_p,dry-air + W×C_p,vapour = 1.005 + 0.02×1.88 = 1.0426 kJ/(kg dry air·K).
Heating from 30°C to 65°C (humidity ratio constant during sensible heating): Q = ṁ_air×C_s×ΔT = 1×1.0426×(65−30) = 1.0426×35 = 36.49 ≈ 36.5 kW. Answer: (B).
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