Okay math friends.
Given a 200 square foot room eight foot ceilings, how long would a 1500 watt / 5100 btu heater need to run to raise the ambient temperature from 80 F to 120 F?
Presume cinder block construction and minimal insulation.
Need answer for a friend.
Thank you.
Well, that makes it easy. The minimal amount of insulation is none at all, and with no insulation at all, the time that would take is forever. There’s some nonzero amount of insulation that’s required to make it even possible.
We’d also need to know the length and width of the room, not just its area.
Unless, of course, it were located in Death Valley or someplace similar, then it would be the next time the temperature outside rise that high.
I’m in HVAC and have to say that “comfort cooling” is 20 Degrees. That is… If its 95 outside, the best you can get inside is gonna be 75 or so depending on several factors.
However, if its heat you want and right now, start a fire in a 55 gallon drum in the room you want heated.
Please keep us posted.
Friend has bedbugs and she thinks she can do a home heat remedy. I want figures to discourage her.
Is the room on the top(or only) floor? What is the ceiling made out of?
And thank you for mixing American and metric measures …
1600 ft[sup]3[/sup] = 45.3 m[sup]3[/sup] … density of air at 30ºC = 1.16 kg m[sup]3[/sup] … so 45.3 x 1.16 = 52.5 kg … heat capacity of air 1.01 kJ kg[sup]-1[/sup] ºC[sup]-1[/sup] … 40º in F = 22.2º in C … so 1.01 x 52.5 x 22.2 = 1,180 kJ …
1,180 kJ ÷ 1.5 kJ sec[sup]-1[/sup] = 787 sec or 13.1 minutes
So about 650 microfortnights is the answer under ideal conditions …
You might have to hot-wire the heater’s thermostat … which is probably unsafe …
Uh, you would also need to know the outside temperature, plus a reasonable guess on the air infiltration rate. And probably a few other things like information on windows, etc.
But why? Are the bedbugs going anywhere while she is heating the room? And if so, isn’t that the point?
That’s the first-order approximation, and assumes the walls/ceiling/floor do not participate in any heat exchange with the room air. If the cinder-block walls need to be heated (and they do), then their thermal mass must be taken into consideration. For a 200-sqft room, assuming it’s square, the inside perimeter is 26 feet, and with a height of 8 feet, we’re talking about ~200 square feet of wall. At 13 pounds per square foot of wall, that’s 2600 pounds (1182 kg) of wall that needs to also be heated up, along with the 53 kg of air in the room. You wouldn’t have to heat all of it, just the half of the wall facing inward. So figure out the heat needed to warm the entire wall, and divide by two:
wall mass = 1182 kg
concrete specific heat = 750 J/(k*kg)
energy to heat entire wall by 40F (22.2C) = 19730250 J
At 1500 watts, that’ll take (19730250/1500 =) 13,154 seconds, or 3.7 hours. Cut that in half, so 1.9 hours on top of the 13 minutes to heat the air in the room.
This ignores heat delivered to (or lost through) the floor and ceiling, and any heat loss through the minimally-insulated walls, and any heat lost through leaks/air exchange, all of which will substantially raise the required total energy input (and may even make it impossible to reach 120F).
Heat is an accepted method of eliminating bedbugs from a residence. You can by commercial-grade heaters for that exact purpose, but they’re high-powered and not cheap. The intent is not to drive the bugs out, but rather to kill them.
Indeed … however the question was how long to “raise the ambient temperature from 80 F to 120 F” … I agree that we’d have to keep adding heat to keep the room at 120ºF … and we’d have to keep adding heat even if the entire house was brought up to 120ºF … unless it’s 120ºF outside in which case we’d need only run fans to blow the hot air in …
Consider a rig on a 100ºF day … if it has an A/C, that A/C will make the inside of our rig nice and cool rather quickly … and yet the dashboard may still be too hot to touch … we don’t have to bring the entire rig down to 65ºF … just the air inside …
As an HVAC guy, I’m sure you know an important factor is also the efficiency of the heating unit, too. Older styles were 80% efficient, but these days they are commonly 96% efficient.
If the walls are massive enough and/or conductive enough, then 1500 watts of heat input may not be enough (at first, or possibly ever) to reach 120F inside the room - that is, for some room temperature less than 120F, the heat loss to the walls may be greater than 1500 watts.
Actually, come to think of it, there’s a simple answer to this question. What climate is your friend in? What kind of winters does she get, and is her furnace up to it? Because it’s just as hard to get a room to 72 degrees in freezing ambient temperatures as it is to get it to 120 degrees in 80 degree ambient temperatures. OK, technically it’d be a little harder to go from 80 to 120, because of radiative heat transfer, but that’s not going to be a significant difference for a typical house.
The only trick would be in faking out the thermostat, because it’s probably not possible to set it to 120 degrees.
I read a blurb from The University of Minnesota about how to get rid of cockroaches … one thing they suggested was, in the middle of winter, turn off your furnace, drain your water pipes and spend a couple weeks living at a neighbor’s house … cockroaches and their eggs don’t survive -40ºF temperatures …
Let’s assume R-value = 1 … which means a U-value of 1 W m[sup]-2[/sup] K[sup]-1[/sup] … so 1 W m[sup]-2[/sup] K[sup]-1[/sup] x 22.2 K x 55.7 m[sup]2[/sup] = 1,240 W …
That makes 3.7 millifortnights … a bit over an hour … I can’t close off my kitchen, but if someone can go ahead and shut the doors, open your oven door and crank it to 350ºF … time how long until the kitchen is 120ºF …
Missed edit window
ETA: I think that R-value we’re assuming is high, so I believe in actual conditions you’re correct, a 1,500 W heater can’t raise the temps from 80º to 120º in such a room, nevermind the windows et al …
I once worked for a guy who was a bit of a cheapskate. He installed lock-boxes over the thermostats, which he’d set at 60 degrees in the winter. It was uncomfortable. So I’d use two ice-packs and an ace-bandage, totally fooling the thermostat.
For the folks talking about fooling the thermostat, I assume the OPs friend has a 5100 BTU space heater she is planning on using.
Sounds logical - if she’s ever let the house cool down to 32 degrees inside, and noted how long it took to bring it up to 72 degrees.
This is probably close enough for a quick and dirty calculation of the heat required.
The quick and dirty calculation is you take the length x width x height of the area to be heated (200 x 8 in this case, or 1600), and multiply that by some factor for the room insulation. Basically, 3 is a very well insulated room in a modern home, and 10 is a barn. That puts your BTU requirements at a minimum of 4800 for a factor of 3, to a maximum of somewhere around 16,000 for a factor of 10.
A 5100 BTU heater is only going to just barely get you there for an extremely well insulated room. For a more common room (an insulation factor of maybe 5 or so), you’ll need more heat, somewhere in the neighborhood of 8,000 BTUs.
In other words, you’ll likely need to have two heaters instead of one.
This is just a quick and dirty way of figuring out how many BTUs you’ll need, but in my experience it ends up being fairly accurate in the real world.
Your typical space heater these days will have a thermal cutoff for safety that will operate at somewhere between 110 deg and 140 deg. If your heater happens to be on the low end of this, you may have difficulty reaching your 120 deg goal even with sufficient BTUs.