Subtopic: Psychrometry – properties of air-water vapour mixture
Question Statement:
For a psychrometric ratio of 1003 J kg⁻¹ K⁻¹, the latent heat of vaporization at the wet bulb temperature of 35 °C is 2418.9 kJ kg⁻¹. The saturation vapour pressure is 19.7 kPa corresponding to the dry bulb temperature of 60 °C. If the relative humidity of air is 20%, the saturation vapor pressure of the air at the wet bulb temperature in kPa will be __________.
Official Answer Key:
5.4 to 5.6
Step-by-Step Solution & Explanation
• Actual vapour pressure of the air, e = RH × es(Tdb) = 0.20 × 19.7 = 3.94 kPa.
• Psychrometric (wet-bulb) equation: e = es(Twb) – A·P·(Tdb–Twb), where A = Cp/(0.622×hfg) is the psychrometric constant, using the given psychrometric ratio (≈Cp) = 1003 J/kg·K, hfg(35°C) = 2,418,900 J/kg, and standard atmospheric pressure P ≈ 101.3 kPa.
• A·P = (1003×101,325)/(0.622×2,418,900) ≈ 0.0675 kPa/°C.
• es(Twb) = e + A·P·(Tdb–Twb) = 3.94 + 0.0675×(60–35) = 3.94 + 1.69 ≈ 5.6 kPa, at the upper edge of the accepted range 5.4–5.6 (the small residual reflects the assumed atmospheric-pressure value, not stated explicitly in the question).
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