Heat Buildup in Complete Insulation Box

[kiki_danc]

Supposed you have a box of size 1 square foot and the insulation is 100% efficient.. meaning there is no transfer of any heat outside.. and you put a lamp with glass surface temperature of say 50 Celsius (155 Fahrenheit). Would the air temperature in the box keep increasing... can it reach 1000 Celsius after days.. or would it be maintain at 50 Celsius only.. and why?

 

[Chestermiller]

How are you supposed to be controlling the surface temperature of the lamp so that it stays at 50 C indefinitely?

 

[kiki_danc]

How are you supposed to be controlling the surface temperature of the lamp so that it stays at 50 C indefinitely?

The lamp is just an example to illustrate any component that can produce constant 50 celsius.

 

[Chestermiller]

Then once it reaches 50, it will stay at 50.

 

[kiki_danc]

Then once it reaches 50, it will stay at 50.

I was referring to the air in the enclosure. Wont the temperature keep increasing if the heat can't get out (assuming the box is a perfect insulator or thermo)

 

[Chestermiller]

I was referring to the air in the enclosure. Wont the temperature keep increasing if the heat can't get out (assuming the box is a perfect insulator or thermo)

No. Not if the lamp stays at 50.

 

[kiki_danc]

No. Not if the lamp stays at 50.

But where will the heat go if it can't escape the box? Remember box is not metal but perfect theoretical insulator.

 

[Chestermiller]

But where will the heat go if it can't escape the box? Remember box is not metal but perfect theoretical insulator.

No heat comes out of the lamp once the air matches the lamp temperature of 50 C. You can’t independently specify both the heat coming out of the lamp and it’s temperature.

 

[kiki_danc]

No heat comes out of the lamp once the air matches the lamp temperature of 50 C. You can’t independently specify both the heat coming out of the lamp and it’s temperature.

Ah, you meant atomic wise, the vibrations of the lamp surface at 50 C will just equilibrate the vibrations in the air. This is reasonable.

Wha counter analogy or other objects or can you give any principle where the surrounding will keep adding up even if the source is constant?

 

[CWatters]

A real light bulb wouldn't stay at 50C. It and the box would get hotter and hotter until something failed.

If you use something else like a thermostat controlled radiator set to 50C the box will heat up until reaches 50C. At that point the heat flow from rad to box and box to rad will be equal. The thermostat will switch off the heater. It will stay like that indefinitely as the insulation is 100% ideal.

 

[CWatters]

Wha counter analogy or other objects or can you give any principle where the surrounding will keep adding up even if the source is constant?

In theory if you connect an inductor to a constant voltage source the current will keep increasing indefinitely. However real world voltage sources can only deliver limited current and real world inductors have resistance and can only carry limited current.

 

[Tom.G]

Wha counter analogy or other objects or can you give any principle where the surrounding will keep adding up even if the source is constant?

That really depends on what you define as the "Source"!

In your initial question, Source was a constant temperature object. That of course creates a constant temperature box interior.

If Source is defined as a 'Constant Energy Input', then the box could reach either infinite temperature or the failure temperature of the box material, whichever occurs first.

Cheers,
Tom

 

[hmmm27]

Wha counter analogy or other objects or can you give any principle where the surrounding will keep adding up even if the source is constant?

There are a few cases where you end up with something at a higher temperature than what you started with... eg:

- if you use a vacuum to boil water at room temperature, the steam drawn off will recondense at normal pressure at 100C.
- the greenhouse effect : sunlight coming in your car window isn't that hot in terms of areal energy, but it builds up inside because the inside objects it hits radiate IR which can't escape through glass.

In what context is your question ?

 

[kiki_danc]

There are a few cases where you end up with something at a higher temperature than what you started with... eg:

- if you use a vacuum to boil water at room temperature, the steam drawn off will recondense at normal pressure at 100C.
- the greenhouse effect : sunlight coming in your car window isn't that hot in terms of areal energy, but it builds up inside because the inside objects it hits radiate IR which can't escape through glass.

In what context is your question ?

Ok. Let's say you have a sealed metal enclosure that measures 20"x13"x12". Let's say there is no ventilation. And you have a power supply inside that gives off constant 50 Celsius surface temperature (let's ignore the wattage transferred into heat or BTU part). At what rate would the air transfer the heat to the metal surface and the metal transferring the heat outside supposed the ambient temperature outside the enclosure is 35 Celsius?

 

[Chestermiller]

There are a few cases where you end up with something at a higher temperature than what you started with... eg:

- if you use a vacuum to boil water at room temperature, the steam drawn off will recondense at normal pressure at 100C.

What exactly are you saying here? How do you propose to get the low temperature steam back to 1 atm? By adiabatically compressing it?

 

[kiki_danc]

That really depends on what you define as the "Source"!

In your initial question, Source was a constant temperature object. That of course creates a constant temperature box interior.

If Source is defined as a 'Constant Energy Input', then the box could reach either infinite temperature or the failure temperature of the box material, whichever occurs first.

Cheers,
Tom

So a power supply is a constant energy input source?

The 51.6 C is just the surface temperature.. there is the watt being converted into heat every minute.. so I guess the power supply in a sealed enclosure (or better yet a perfect theoretical insulator) would just keep increasing in temperature until it breaks. ?

 

[Chestermiller]

Ok. Let's say you have a sealed metal enclosure that measures 20"x13"x12". Let's say there is no ventilation. And you have a power supply inside that gives off constant 50 Celsius surface temperature (let's ignore the wattage transferred into heat or BTU part). At what rate would the air transfer the heat to the metal surface and the metal transferring the heat outside supposed the ambient temperature outside the enclosure is 35 Celsius?

This is a pretty complicated problem that would involve convective heat transfer from the box to the surrounding air at 35C (and a small amount of radiative heat transfer). If the exterior convection is vigorous enough, the outside surface temperature of the box will be 35C. Are you willing to make this approximation? Inside the box, there will be natural convection as a mechanism for transferring heat from the lamp to the air and, from the air to the walls of the box. To calculate the rate of heat transfer from the lamp to the air, you need to know the heat transfer coefficient from the lamp to the air. This will depend on the detailed geometry of the lamp and the placement of the lamp within the box. Knowing these, it is possible to determine the rate of heat transfer from the lamp to the air and from the air to the walls of the box using computational fluid dynamics. The temperature at the inside walls of the box will vary with position on the walls. To complete the calculation, you would also include the heat transfer through the walls of the box, and how that couples with the temperature variations inside and outside (resulting from the natural convection inside). This would require knowledge of the wall thicknesses and the thermal properties of the walls (including change in storage of heat in the walls).

Is this a solvable problem? Yes. Are there approximations that can be made to solve this problem more easily? Yes, but not without having a decent estimate of the heat transfer coefficient at the lamp and at the wall.

 

[kiki_danc]

No. Not if the lamp stays at 50.

Going back to this lamp at 50 C and a perfect insulator box. Isn't it there is continuous input of energy to the lamp. So the temperature won't remain 50C but keeps increasing? and if the box is a perfect insulator.. the air inside can really reach 1000 Celsius if the temperature of the lamp becomes 1000 Celsius?

Or if lamp can't do this (why can't it keep increasing in temperature?). Let's take the case of power supply. If it is 90% efficient. 10% is converted to heat.. so I guess the temperature can keep increasing until the air in the prefect insulator box reaches 1000 Celsius?

 

[hmmm27]

What happens is that whatever the amount of heat being produced by the PS is the amount that eventually will be emitted by the surface of the container.

 

[kiki_danc]

What happens is that whatever the amount of heat being produced by the PS is the amount that eventually will be emitted by the surface of the container.

To gain more in depth understanding of the principle.. what if the container couldn't emit any heat outside or perfect insulator. Could the air inside the perfect insulator box keep increasing in temperature until it reaches 1000 Celsius (supposed the power supply can take this temperature)?

 

[Chestermiller]

Going back to this lamp at 50 C and a perfect insulator box. Isn't it there is continuous input of energy to the lamp. So the temperature won't remain 50C but keeps increasing? and if the box is a perfect insulator.. the air inside can really reach 1000 Celsius if the temperature of the lamp becomes 1000 Celsius?

You said the lamp is always at 50 C. Now you're changing that?

Or if lamp can't do this (why can't it keep increasing in temperature?). Let's take the case of power supply. If it is 90% efficient. 10% is converted to heat.. so I guess the temperature can keep increasing until the air in the prefect insulator box reaches 1000 Celsius?

In the real world, if you keep supplying energy to the lamp, its temperature (and that of the air) will continue to increase.

 

[Chestermiller]

To gain more in depth understanding of the principle.. what if the container couldn't emit any heat outside or perfect insulator. Could the air inside the perfect insulator box keep increasing in temperature until it reaches 1000 Celsius (supposed the power supply can take this temperature)?

Sure. What did you expect?

 

[kiki_danc]

You said the lamp is always at 50 C. Now you're changing that?

In the real world, if you keep supplying energy to the lamp, its temperature (and that of the air) will continue to increase.

So you mean if my living room was a perfect insulator, the lamp in the ceiling would keep increasing in temperature until the room air reaches hundreds of degrees of Celsius even if the lamp was just a 10 LED light bulb?

 

[kiki_danc]

You said the lamp is always at 50 C. Now you're changing that?

When I said the lamp was always at 50 C. I was referring to a lamp in open air at constant 50 C. But taken to a sealed enclosure, I realized it was automatically no longer a constant 50 C.. but would increase. The take home lesson is that never put power supply inside sealed enclosure without adequate ventilation or without computation that the enclosure can radiate off the heat with good safe margin. Back to real life metal enclosure. Do you have know java site that computes them depending on the composition of the metal, etc.?

 

[gmax137]

Please read Chet's Post #17. I seriously doubt you will find "a java site" that can ask/guess at all the inputs necessary for a specific situation.

If you need to know the temperature inside some specific enclosure, you could:
1) study an engineering heat transfer book so you know how to solve the problem
2) get an engineer to calculate it for you
3) build your box and install a thermometer in it to measure the temperature

 

[kiki_danc]

Please read Chet's Post #17. I seriously doubt you will find "a java site" that can ask/guess at all the inputs necessary for a specific situation.

If you need to know the temperature inside some specific enclosure, you could:
1) study an engineering heat transfer book so you know how to solve the problem
2) get an engineer to calculate it for you
3) build your box and install a thermometer in it to measure the temperature

My solution is simply to put the power supply outside.. I couldn't take any chance with sealed enclosure so my interest in the above is simply theoretical only. Someday if somehow we could extract energy from the vacuum, I guess the Earth would overheat and accelerated greenhouse effect. The knowledge in the sealed enclosure dynamics can give us insight how it would behave.

 

[CWatters]

Going back to this lamp at 50 C and a perfect insulator box. Isn't it there is continuous input of energy to the lamp. So the temperature won't remain 50C but keeps increasing? and if the box is a perfect insulator.. the air inside can really reach 1000 Celsius if the temperature of the lamp becomes 1000 Celsius?

Yes a real light bulb will keep increasing in temperature but you told us that the lamp was...

...just an example to illustrate any component that can produce constant 50 celsius.

You need to be clearer.

 

[kiki_danc]

Yes a real light bulb will keep increasing in temperature but you told us that the lamp was...
You need to be clearer.

When I didn't make my question clear and Chestermiller replied it would be constant. I actually imagined the enclosure would stop the temperature from increasing. I imagined it was like the enclosure was filled with water (which stands for temperature), and the source of water at center couldn't push it back anymore because the enclosure enclosing it was stronger. So I was thinking maybe the 50 Celsius in the power supply will just stay that way throughout the enclosure as it equilibrate with air inside. When you guys emphasized it would really increase to 1000 Celsius as I imagined. Then I made full stop and would no longer put the power supply inside a sealed enclosure. I'm sharing so you would know how a physics illiterate or newbie would think.

Well going back to the water analogy. Is there a temperature.. maybe one billion degree Celsius.. that it could act like the water analogy where it couldn't increase anymore because the stronger enclosure wall was pushing it? Or would the temperature need to fill up the Planck scale before it could do that? And since the universe can fit inside the Planck scale.. then it's not possible for temperature inside our universe to act like the water analogy?

 

[CWatters]

When I didn't make my question clear and Chestermiller replied it would be constant. I actually imagined the enclosure would stop the temperature from increasing. I imagined it was like the enclosure was filled with water (which stands for temperature), and the source of water at center couldn't push it back anymore because the enclosure enclosing it was stronger. So I was thinking maybe the 50 Celsius in the power supply will just stay that way throughout the enclosure as it equilibrate with air inside. When you guys emphasized it would really increase to 1000 Celsius as I imagined. Then I made full stop and would no longer put the power supply inside a sealed enclosure. I'm sharing so you would know how a physics illiterate or newbie would think.

Well going back to the water analogy. Is there a temperature.. maybe one billion degree Celsius.. that it could act like the water analogy where it couldn't increase anymore because the stronger enclosure wall was pushing it? Or would the temperature need to fill up the Planck scale before it could do that? And since the universe can fit inside the Planck scale.. then it's not possible for temperature inside our universe to act like the water analogy?

If the insulation is 100% efficient (so no power leaks out) and there is still power going in then the temperature will keep rising.

In the real world the insulation isn't perfect so the temperature rises until the power leaking out equals the power going in.

To use the water analogy... If you dam a river totally the water will keep rising. If you have a hole in the dam the water rises increasing the pressure and flow rate through the hole until the flow rate leaving matches that arriving. How high it gets depends on both the incoming flow rate and how the outgoing flow rate responds to increasing pressure.

 

[kiki_danc]

If the insulation is 100% efficient (so no power leaks out) and there is still power going in then the temperature will keep rising.

In the real world the insulation isn't perfect so the temperature rises until the power leaking out equals the power going in.

To use the water analogy... If you dam a river totally the water will keep rising. If you have a hole in the dam the water rises increasing the pressure and flow rate through the hole until the flow rate leaving matches that arriving. How high it gets depends on both the incoming flow rate and how the outgoing flow rate responds to increasing pressure.

Ok. In my country. The ambient outdoor temperature can reach up to 42.2 Celsius. So indoor it could reach 45 Celsius. The operating temperature of the power supply is only -40 C to +40 C. So if it would be kept inside the enclosure. Even if the metal box can let the heat out.. it would be met with 45 Celsius worse case scenario. So the most logical is not to use any enclosure.

Now my problem is If I just put it on the surface say a table exposed to open air. If the ambient temperature of open indoor air is 42 Celsius. And the operating range of the power supply is only up to 40 Celsius. What do you think would happen to the 50 Celsius average temperature of the power supply surface.. would it increase to 55 Celsius or remain at 50 Celsius because the ambient temperature of 42 Celsius is still lower than it so it can still produce an air heat sink?