Answer:
1.57 kW
Explanation:
The rate of heat loss is given by:
q = Gm * Cp * (tfin - ti)
Where
q: rate of heat loss
Gm: mass flow
Cp: specific heat at constant pressure
The Cp of air is:
Cp = 1 kJ/(kg*K)
The mass flow is the volumetric flow divided by the specific volume
Gm = Gv / v
The volumetric flow is the air speed multiplied by the cruss section of the duct.
Gv = s * h * w (I name speed s because I have already used v)
The specific volume is obtained from the gas state equation:
p * v = R * T
60 C is 333 K
The gas constant for air is 287 J/(kg*K)
Then:
v = (R * T)/p
v = (287 * 333) / 100000 = 0.955 m^3/kg
Then, the mass flow is
Gm = s * h * w / v
And rthe heat loss is of:
q = s * h * w * Cp * (tfin - ti) / v
q = 5 * 0.25 * 0.2 * 1 * (54 - 60) / 0.955 = -1.57 kW (negative because it is a loss)
