3 ms·

Sphere's surface grows as radius squared, but volume grows as radius cubed. Hence a small terrarium will quickly freeze, and a huge terrarium will eventually fr

• tbrownaw 1y ago
  What does volume have to do with energy balance?
  • thfuran 1y ago
    Heat is transferred through the surface area and produced by the volume (assuming there's something going on in the system that's exothermic).
    • jjk166 1y ago
      Heat isn't produced by the volume. Heat may be produced by something within the volume, but it's not the volume's existence that causes heat to be produced. There is no fundamental reason a bigger terrarium should produce more heat, nonetheless that heat production should be directly proportional to volume.
      • thfuran 1y ago
        Yes, obviously it'd be the stuff in the terrarium rather than the space it occupies that produces heat, but the amount of stuff you can fit in it is determined by the occupiable space. And if that stuff is producing heat, such as by decay, there's going to be more heat with more stuff. Though even if it cooks itself for a while, it should eventually settle on a temperature determined mostly by orbital parameters and material properties rather than size, since the stuff can't be net exothermic forever. But greater atmospheric depth probably still increases equilibrium temperature by reducing heat transfer through that side of the terrarium.
        • jjk166 1y ago
          > but the amount of stuff you can fit in it is determined by the occupiable space. You can fit more into a larger terrarium, but that doesn't require a larger terrarium to contain more. Regardless of what is contained within the terrarium, it's heat production is limited by what it receives from the environment. > But greater atmospheric depth probably still increases equilibrium temperature by reducing heat transfer through that side of the terrarium. Greater atmospheric depth affects heat transfer by changing the density of the atmosphere, which is relevant for an atmosphere held to a body by gravity, but not for one contained in a pressurized vessel like a terrarium. A terrarium with a 1 atm internal pressure has an atmosphere depth equal to earth's atmosphere regardless of size (at least up until the point where the terrarium's gravity is comparable to a planet).
          • thfuran 1y ago
            >You can fit more into a larger terrarium, but that doesn't require a larger terrarium to contain more. Regardless of what is contained within the terrarium, it's heat production is limited by what it receives from the environment. Go make a pile of mulch and monitor the temperature at the center. You will find that after a while it is hotter than ambient by a large margin because it is generating heat. The more mulch you permit to decay, the more heat will be generated. >Greater atmospheric depth affects heat transfer by changing the density of the atmosphere Greater atmospheric depth affects heat transfer by increasing the chances that an outbound photon of black body radiation hits a molecule that will absorb it and later re-emit the energy as black body radiation in a random direction, only sometimes still in a direction that will escape. It’s true that increasing atmospheric density will increase the chances of an outbound photon being absorbed, but so will increasing the distance the photon has to travel through atmosphere of any given density. The deeper the bubble of air, the more re-absorption.
• askvictor 1y ago
  Is there a 'just right' size that neither freezes nor fries?
  • thfuran 1y ago
    About Earth sized, I think. A bit bigger if the soil is low on hot isotopes.
• hparadiz 1y ago
  I imagine one like that in my kitchen which is currently moss, a succulent, and some weed that happened to germenate. All three are alive after two years so far. The bottom is rocks and soil. There's a clear water cycle too as water evaporates and collects on the surface of the glass and then drips down.
• jjk166 1y ago
  That's not how space or terrariums work. A terrarium does not spontaneously produce energy out of nothing, it gets energy from the sun. Heat input from the sun is proportional to cross sectional area, while heat loss to space is proportional to surface area, which scale the same for a sphere. A larger object will have more thermal mass which would make it take longer to change its temperature, but it will still have the same thermal equilibrium. Terrariums do not need to be spheres, so the volume does not necessarily scale as the radius cubed.
  • IAmBroom 1y ago
    Terarriums do not need to be spheres, but that is the only reasonable shape when it costs $Ms to get the glass up there in the first place.