How do things expand (due to heat)?

[SpY]]

I just started thermodynamics and I can get the concepts its just application that's a bit hard. It makes sense that most objects will expand when you heat them up. I'm not sure this is the exact reason, but is it because the particles gain more energy to move around faster and repel each other more?

Also there are few cases of expansion which I can't understand (without experiment)
1. A liquid L in a closed container C with 2 different conductivities.
If [tex] \kappa_L = 0[/tex] but the container expands, what will happen to the liquid?
If [tex] \kappa_C = 0[/tex] but the liquid expands, will it break the container?

2. This is quite similar, but suppose it's now a glass of beer :)
Both have different non-zero conductivities, but is there a way to find how much beer spills over, or how much more volume is made available (due to expanding glass)

3. I think I asked this before but it still doesn't make sense. A rectangular plate with a circular hole heats up and expands... what happens to the hole?
Apparently it will decrease, but I'm thinking it will get bigger because the whole plate would just scale up and expand in all directions ??

(just a quick question on TD equilibrium: a 5°C in a 25° room will warm up to 25°C at equilibrium?)

Thanks

 

[mikelepore]

I only know a small part of the answers:

It makes sense that most objects will expand when you heat them up. I'm not sure this is the exact reason, but is it because the particles gain more energy to move around faster and repel each other more?

In any solid the distance between atoms or molecules is a position of balance between attractive and repulsive forces. If they get any closer they will experience more repulsion, and if they get any further apart they will experience more attraction. Therefore the equilibrium position is a relative minimum in potential energy. That's the process that the increased bond vibration amplitude, which higher temperature represents, is messing with. To have a greater amplitude of vibration is a form of looser bonding, so the equilibrium distance is further out. I don't know any more that that, and I'm looking forward to seeing what other writers can add.

3. I think I asked this before but it still doesn't make sense. A rectangular plate with a circular hole heats up and expands... what happens to the hole?
Apparently it will decrease, but I'm thinking it will get bigger because the whole plate would just scale up and expand in all directions ??

The entire object scales up, so the hole retains its original shape and increases in size by the same proportion that the other dimensions of the material increase in size.

What I said is not exactly right for all materials. A few materials which are called anisotropic have different coefficients of linear thermal expansion in different dimensions, because of the structure. Graphite is anisotropic, due to it structure of having layers of two-dimensional sheets of atoms rather than a three-dimensional periodicity. Depending on the orientation, that might cause a circular hole to become elliptical as the object expands.

 

[Dr Lots-o'watts]

is it because the particles gain more energy to move around faster and repel each other more?

Yes.

Also there are few cases of expansion which I can't understand (without experiment)
1. A liquid L in a closed container C with 2 different conductivities.

Conductivities? Or do you mean expansion coefficients?

3. I think I asked this before but it still doesn't make sense. A rectangular plate with a circular hole heats up and expands... what happens to the hole?
Apparently it will decrease, but I'm thinking it will get bigger because the whole plate would just scale up and expand in all directions ??

No, it doesn't just scale up, it just takes up more volume in any direction it can. Just imagine the plate is made of bees instead of atoms.

(just a quick question on TD equilibrium: a 5°C in a 25° room will warm up to 25°C at equilibrium?)

Both will average out to around 24.9 or so.

 

[Mapes]

I just started thermodynamics and I can get the concepts its just application that's a bit hard. It makes sense that most objects will expand when you heat them up. I'm not sure this is the exact reason, but is it because the particles gain more energy to move around faster and repel each other more?

No. Just moving faster or with a larger amplitude would not cause bulk expansion if the atoms existed in a symmetric energy well. The reason most objects expand with heating is that the energy well that governs atomic spacing is asymmetric; see http://books.google.com/books?id=Ze...mal expansion asymmetric energy well&f=false", for example.

Also there are few cases of expansion which I can't understand (without experiment)
1. A liquid L in a closed container C with 2 different conductivities.
If [tex] \kappa_L = 0[/tex] but the container expands, what will happen to the liquid?
If [tex] \kappa_C = 0[/tex] but the liquid expands, will it break the container?

Do you mean thermal expansion coefficient [itex]\alpha[/itex] here? (There's no connection between thermal expansion and thermal conductivity [itex]\kappa[/itex].) If the container expands more than the liquid, the liquid will boil. If the liquid expands more than the container, the container may break or the liquid may solidify.

3. I think I asked this before but it still doesn't make sense. A rectangular plate with a circular hole heats up and expands... what happens to the hole?
Apparently it will decrease, but I'm thinking it will get bigger because the whole plate would just scale up and expand in all directions ??

It depends on the boundary conditions at the edge of the plate. If the plate is unconstrained, the hole will expand as the plate expands. What do you think will happen if the edges of the plate are fixed?

 

[SpY]]

Sorry, I totally confused the two concepts, I meant expansion coefficients, thanks!
1. A liquid L in a closed container C with 2 different expansion coeffecients [tex]/alpha_1 , /alpha_2[/tex].

[QUOTE name='Dr Lots-owatts']No, it doesn't just scale up, it just takes up more volume in any direction it can. Just imagine the plate is made of bees instead of atoms.[/QUOTE]

[QUOTE name-'Mapes']It depends on the boundary conditions at the edge of the plate. If the plate is unconstrained, the hole will expand as the plate expands. What do you think will happen if the edges of the plate are fixed?[/QUOTE]

The question is when it's unrestricted. I'm quite sure if you're saying the same thing, but if it expands in any direction, the plate would expand outwards perpendicular to every surface - including inwards, which makes the hole smaller. But Mapes says otherwise :/
(If the edges are confined then I guess it would expand inwards, decreasing the hole)

 

[Mapes]

[QUOTE='SpY]The question is when it's unrestricted. I'm quite sure if you're saying the same thing, but if it expands in any direction, the plate would expand outwards perpendicular to every surface - including inwards, which makes the hole smaller. [/QUOTE]

Nope; it's not the case that thermal expansion implies perpendicular outward deformation at every surface. If the plate is unconstrained, then it remains absolutely stress-free under any temperature change. That means we could cut a hole anywhere (or fill any hole) and the deformation would be exactly the same. Therefore, each hole expands exactly as it would if it were filled.