How Does Temperature Change in a Sealed Room with a Broken Cooling System?

[skpmobile]

Base temperature 68F
BTU - 8000
Cubic Feet of Air -10000

Coolign mechanism fails.
No air circulation.
Closed air space.

Starting at 68F what is the formula to calculate the temperature curve over time?

 

[Danger]

Welcome to PF, Skpmobile, but please don't double-post. You've already asked this in General Physics. It will be dealt with when someone with the answer gets around to it. I don't know it myself.

 

[Jack111]

F? BTU? cubic feet?

Sounds like Newton's law of cooling here but you're going to need to flesh it out a bit and convert all units to SI first

 

[Astronuc]

Base temperature 68F
BTU - 8000
Cubic Feet of Air -10000

Coolign mechanism fails.
No air circulation.
Closed air space.

Starting at 68F what is the formula to calculate the temperature curve over time?

I'm afraid I cannot make sense of the problem as posed. What is supposed to happen with 8000 BTU?

Cooling mechanism fails? If there is no heat transfer, there is no temperature change.

No air circulation would imply no convection.

Radiative heat transfer would occur, but that is very slow, and it depends on the temperature differential or rather T_hot⁴-T_cold⁴

Without radiation and convection, one is left with conduction, but the problem states no cooling.

Does the problem infer putting 8000 BTU into 10000 cu ft of air with adiabtic boundary conditions?

 

[FredGarvin]

That's the way I am reading it. A 10,000 ft^3 volume at an initial 68°F with a Q = 8000 BTU input.

First Law stuff.

 

[skpmobile]

Clarification

I'm afraid I cannot make sense of the problem as posed. What is supposed to happen with 8000 BTU?

Cooling mechanism fails? If there is no heat transfer, there is no temperature change.

No air circulation would imply no convection.

Radiative heat transfer would occur, but that is very slow, and it depends on the temperature differential or rather T_hot⁴-T_cold⁴

Without radiation and convection, one is left with conduction, but the problem states no cooling.

Does the problem infer putting 8000 BTU into 10000 cu ft of air with adiabtic boundary conditions?

For Example:
I have a room with 8000 cubic feet of air in the room
There is equipment in the room that is generating 100BTUs
I currently have chillers in that room to cool it to 68F
If those chillers fail starting at 68F what would be the temperature increase over time?

 

[Astronuc]

OK - that is a better description of the problem. It can be handled by a 'lump parameter' model, i.e. time dependent heat transfer in basically zero dimensions.

One is looking at heat source and loss of heat transfer from the system, so the internal energy, and therefore temperature, increases with time.

 

[skpmobile]

Great, so what equation would i plug those paraketers into to calculate points on the curve?

 

[Astronuc]

Well, are the chillers failing one by one, or all together.

One has to determine the rate at which energy is accumulating, which is the difference between heat generation and heat loss. Then relate that to specific heat of the air.

I could be as simple as - http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/spht.html

http://hyperphysics.phy-astr.gsu.edu/hbase/kinetic/shegas.html

Think about how to make Q\,=\,cm\Delta{T} time dependent.

 

[skpmobile]

Points of clarification:
- fixed volume of air (closed room)
-starting air temperature is 68F
-cubic feet is the measurement of the air
-standard air
-no air movement generated with the exception of thermally generated
movement
-chillers all fail at once (instant loss of cooling ability)
- Thermal factor (BTU) derived from equipment documentation
-maximum for that equipment (looking at a worst case scenario)

So if I understand your statement I would have a constant level of heat being generated (the BTUs) and no heat loss from that environment. So I am looking at generating a curve of heat increase, so my x-axis is time ( 1 minute increments ) and my y-axis is temperature ( 1 degree increments ) where do I go from here?

 

[quark]

The equipment rating should be in btu/hr rather than btu. Use the formula Q = 1.1xcfmxdT. As you have no air circulation, after adding up all the heatloads in the room and getting the total heat input in btu/hr, divide the room volume by 60. This gives you the temperature rise per minute.

 

[skpmobile]

Gentlemen, I am a total laymen relative to physics would you be so kind as to plug my original numbers into the appropriate places in the equation so I have a clearer picture. Your assistance is greatly appreciated.

 

[skpmobile]

Astronuc, I finally think I am getting it I just don't know how to determine time by the equation.

284064031.4... 21851079.33... 1.3... 10
Q...... C......Mass of...Temperature
.........Air at SL...Delta

 

[Danger]

Great, so what equation would i plug those paraketers into to calculate points on the curve?

Once you start plugging things into parakeets, you're out of the realm of physics and getting into abnormal psychology. There are people here who can help you with that as well.