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B Heat Buildup in Complete Insulation Box

  1. Oct 26, 2018 #1
    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?
  2. jcsd
  3. Oct 26, 2018 #2
    How are you supposed to be controlling the surface temperature of the lamp so that it stays at 50 C indefinitely?
  4. Oct 26, 2018 #3
    The lamp is just an example to illustrate any component that can produce constant 50 celsius.
  5. Oct 26, 2018 #4
    Then once it reaches 50, it will stay at 50.
  6. Oct 26, 2018 #5
    I was referring to the air in the enclosure. Wont the temperature keep increasing if the heat cant get out (assuming the box is a perfect insulator or thermo)
  7. Oct 26, 2018 #6
    No. Not if the lamp stays at 50.
  8. Oct 26, 2018 #7
    But where will the heat go if it cant escape the box? Remember box is not metal but perfect theoretical insulator.
  9. Oct 26, 2018 #8
    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.
  10. Oct 26, 2018 #9
    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?
  11. Oct 27, 2018 #10


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    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.
  12. Oct 27, 2018 #11


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    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.
  13. Oct 27, 2018 #12


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    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. :wink:

  14. Oct 27, 2018 #13

    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 ?
  15. Oct 27, 2018 #14
    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?
  16. Oct 27, 2018 #15
    What exactly are you saying here? How do you propose to get the low temperature steam back to 1 atm? By adiabatically compressing it?
  17. Oct 27, 2018 #16
    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. ?
  18. Oct 27, 2018 #17
    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.
  19. Oct 27, 2018 #18
    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?
  20. Oct 27, 2018 #19
    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.
  21. Oct 27, 2018 #20
    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)?
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