I am working on a problem where I need to determine the time taken for an air heater with an 8kW output to heat a volume of air of 9m^3 by 25C. I am neglecting all losses at the moment. It almost seems too simple in my mind that I'm concerned I'm overlooking something.
cp = 1005 J kg-1 K-1
ρ = 1.534 kg m-3
Q = cp * m * dT
The Attempt at a Solution
Q = 1005 * (1.534 * 9) * 25 = 346875.75 J = 0.35MJ
As 1kWh = 3.6MJ:
0.35 / 3.6 = 0.097kWh required for a dT of 25C to heat a 9m^3 volume of air.
The time required would therefore be 0.097 / 8 = 0.012 hours or approximately 43 seconds.
Am I along the right lines here?