Question

For an air-conditioned space, RTH = 100 kW, RSHF = 0.75, volume flow rate of air is 100 m³/minute and room specific humidity is 0.01 kg/kg of dry air. The specific humidity of supply air in kg/kg of dry air is

1. 0.0100
2. 0.0075
3. 0.0050
4. 0.0025

Answer 1

Correct Answer - Option 3 : 0.0050

Concept:

RSHF (Room Sensible Heat Factor): It is defined as sensible heat load divided by total heat load in a room.

RTH = Room Total Heat, RSH = Room Sensible Heat, RLH = Room Latent Heat.

RTH = RSH + RLH ……….(I)

\({\bf{RSHF}} = \frac{{{\bf{RSH}}}}{{{\bf{RTH}}}} \) ..... (II)

RLH = 50 × cmm × (ω₁ – ω₂) .....(III) 

where, cmm is cubic meter per minute i.e., air changes per minute.

ω₁, ω₂ = specific humidity of the room and supplied air.

Calculation:

Given:

RSHF = 0.75, RTH = 100 kW, Air changes per minute = 100 m³/min ⇒ 100 × 10⁶ cm³/min.

By using equation (II)

\({{RSHF}} = \frac{{{{RSH}}}}{{{{RTH}}}} \)

RSH = 0.75 × 100 kW = 75 kW.

By using equation (I)

RTH = RSH + RLH

RLH = 100 – 75 = 25 kW.     

By using equation (III)

RLH = 50 × cmm × (ω1 – ω2)

25 = 50 × 100 × (ω₁ - ω₂)

(ω1 - ω2) = 0.005

0.01 - ω2 = 0.005

ω₂ = 0.05 kg/kg of dry air.