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

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Discussion Overview

The discussion revolves around the temperature change in a sealed room following the failure of a cooling system. Participants explore the implications of a closed air space with no air circulation and the introduction of heat from equipment, seeking to understand the temperature curve over time under these conditions.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • Some participants suggest that the problem may involve Newton's law of cooling, but emphasize the need for unit conversion to SI.
  • There is uncertainty about the role of the 8000 BTU input and whether it implies heat generation in the absence of cooling.
  • One participant notes that without heat transfer, there would be no temperature change, questioning the assumptions of the problem.
  • Another participant proposes a 'lump parameter' model to analyze the heat transfer dynamics, indicating that internal energy and temperature would increase over time.
  • Clarifications are made regarding the fixed volume of air, the initial temperature, and the nature of heat generation versus heat loss.
  • Participants discuss the need to determine the rate of energy accumulation, considering both heat generation and potential heat loss, and relate it to the specific heat of air.
  • One participant suggests using the formula Q = 1.1 x cfm x dT to calculate temperature rise per minute, given the lack of air circulation.
  • A request for assistance in applying the original numbers to the equations is made by a participant unfamiliar with the physics involved.

Areas of Agreement / Disagreement

Participants express differing views on the interpretation of the problem, particularly regarding the implications of the BTU input and the conditions of heat transfer. There is no consensus on a definitive approach or formula to calculate the temperature curve.

Contextual Notes

Participants highlight limitations in the problem's assumptions, such as the lack of clarity on heat transfer mechanisms and the conditions under which temperature changes occur. The discussion remains open to interpretation and refinement.

skpmobile
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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?
 
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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.
 
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
 
skpmobile said:
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 Thot4-Tcold4

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?
 
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.
 
Clarification

Astronuc said:
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 Thot4-Tcold4

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?
 
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.
 
Great, so what equation would i plug those paraketers into to calculate points on the curve?
 
Last edited:
  • #10
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?
 
  • #11
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.
 
  • #12
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.
 
  • #13
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
 
  • #14
skpmobile said:
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.
 

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