2 years, 7 months ago
How long will it take to warm up my bathroom in the morning?
I have:
* a 1500W electrical heater
* bathroom dimensions: 5ft x 9ft x 8ft
* warming up is defined as raising the temperature in the bathroom by 10 degrees Fahrenheit.
* a 1500W electrical heater
* bathroom dimensions: 5ft x 9ft x 8ft
* warming up is defined as raising the temperature in the bathroom by 10 degrees Fahrenheit.
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M$1 Answer
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
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
You can leave an optional "tip" with Mahalo's virtual currency, Mahalo Dollars. If you are asking a difficult question that might require some research, or if you'd like a wide variety of feedback, a higher tip often leads to more answers to your question.
M$
Thanks, your math looks correct.
But, my experience is that it seems to take more than 2 minutes to heat my bathroom in the morning.