Since you're trying to heat up your bathroom with a space heater, I'm assuming it's fairly cold to start with. Somewhere around 60 degrees F (~15.6 degrees C) would meet that criteria for me, so I'll use that.

Then, use Q = mcΔT
(Q = total heat used to heat the room by 10 degrees F (12.2 Celsius)
m = the mass of the air in the room
c = heat capacity of air
ΔT = change in temperature (in your case 10 Fahrenheit or 12.2 Celsius))

The real question is what is the mass of the air?

In general, density = m / V, so m = (density)*V

The density of air at about 15 Celsius is 1.225 kg / m^3 if you trust Wikipedia (which I'll use for the sake of time)

Given that your volume is V = 5(9)(8) ft^3 = 360 ft^3 = 10.2 m^3, this means that the mass of air in the room at 15 Celsius is
m = (1.225)(10.2) kg = 12.495 kg

Next, take the specific heat of dry air to be 1.0 kJ / (kg Celsius), so

Q = (12.495 kg)(1.0 kJ / kg Celsius)(12.2 Celsius) = 157929 Joules

Your heater supplies a power of P = 1500 W = 1500 J / s, so

time, t = Q / P = 157929 J / 1500 W = 105.3 s = 1.75 min

Just under two minutes if the room is 60 degrees Fahrenheit
Source(s):
http://en.wikipedia.org/wiki/Density_of_air
http://www.engineeringtoolbox.com/air-specific-heat-capacity-d_705.html


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