# do rubber bands expand or contract when you cool them at constant tension?

#### Darien

##### Platinum Member
?

I'm not sure if I'm doing my calculations correctly because I don't even know intuitively how it works I don't even have a rubber band to test this with

Edit: i think they expand when cooled. see reasoning on bottom

#### WinkOsmosis

##### Banned
Wouldn't that depend on the amount of tension?

#### KingNothing

##### Diamond Member
Why would they expand? Things contract when they get colder.

Originally posted by: KingNothing
Why would they expand? Things contract when they get colder.
Not everything.

#### everman

##### Lifer
Length of the band may increase, but the rubberband itself is contracting. Isn't it?

#### KingNothing

##### Diamond Member
Originally posted by: KingNothing
Why would they expand? Things contract when they get colder.
Not everything.
Except for water, what?

#### Darien

##### Platinum Member
Originally posted by: KingNothing
Why would they expand? Things contract when they get colder.
not always. ice water is less dense than liquid water

#### WinkOsmosis

##### Banned
Originally posted by: Darien
Originally posted by: KingNothing
Why would they expand? Things contract when they get colder.
not always. ice water is less dense than liquid water
That's because it forms big crystals, not because colder water is less dense than warmer water.

#### rgwalt

##### Diamond Member
Is this some sort of crazy mechanical engineering question?

Do you know how elasticity changes with temperature?

R

#### rgwalt

##### Diamond Member
Originally posted by: WinkOsmosis
Originally posted by: Darien
Originally posted by: KingNothing
Why would they expand? Things contract when they get colder.
not always. ice water is less dense than liquid water
That's because it forms big crystals, not because colder water is less dense than warmer water.
Water is most dense at 4 C.

R

#### KingNothing

##### Diamond Member
Originally posted by: rgwalt
Is this some sort of crazy mechanical engineering question?

Do you know how elasticity changes with temperature?

R
If I have gum in my mouth and take a drink of cold water, the gum gets hard. So I would think that elasticity would go down with temperature.

#### Darien

##### Platinum Member
Originally posted by: rgwalt
Is this some sort of crazy mechanical engineering question?

Do you know how elasticity changes with temperature?

R
thermodynamics question.

if I say dE = dQ - dW...and say dQ = 0 since it's adiabatic, I get

dE = -dW = -pdV = dTc_v

but since it's tension and length I'm dealing with

FdL = dTc_v

so expansion when the temperature increases, contraction when the temperature decreases

I just need to know if this is actually what happens...otherwise I screwed up somewhere

#### rgwalt

##### Diamond Member
Originally posted by: KingNothing
Originally posted by: rgwalt
Is this some sort of crazy mechanical engineering question?

Do you know how elasticity changes with temperature?

R
If I have gum in my mouth and take a drink of cold water, the gum gets hard. So I would think that elasticity would go down with temperature.
Well, my guess would be that the rubber band would contract when cooled under constant tension. I imagine this setup as having a piece of rubber band between two clips. The tension is set at some value, and a controller moves the clips to maintain a constant tension in the rubber band. As the rubber band cools, the elasticity goes down, and the tension goes up. Therefore, the clips would have to move inward, allowing the rubber band to contract, in order to maintain a constant tension.

I could be wrong. I'm not a mechanical engineer. I am a chemical engineer, so I know the word "adiabatic", but I have a feeling that you are using the word in a different way than I'm using it.

R

#### rgwalt

##### Diamond Member
Originally posted by: Darien
Originally posted by: rgwalt
Is this some sort of crazy mechanical engineering question?

Do you know how elasticity changes with temperature?

R
thermodynamics question.

if I say dE = dQ - dW...and say dQ = 0 since it's adiabatic, I get

dE = -dW = -pdV = dTc_v

but since it's tension and length I'm dealing with

FdL = dTc_v

so expansion when the temperature increases, contraction when the temperature decreases

I just need to know if this is actually what happens...otherwise I screwed up somewhere
Interesting thermo question. What class is this for? I am unfamilar with the term -pdV = dTc_v. I understand -pdV being the work done due to a volume change at a constant pressure, but what is dTc_v?

Ryan

#### Darien

##### Platinum Member
c_v = specific heat at constant volume

= T * (dS/dT) at constant volume

since dE = TdS - PdV, setting constant volume would mean dE = TdS

dE/dT = Tds/dT = c_v

so dE = dT*c_v

though this is probably wrong, since I use the argument that dV is constant....would mean hell to my problem since that's the change I'm looking for

#### WinkOsmosis

##### Banned
Originally posted by: rgwalt
Originally posted by: WinkOsmosis
Originally posted by: Darien
Originally posted by: KingNothing
Why would they expand? Things contract when they get colder.
not always. ice water is less dense than liquid water
That's because it forms big crystals, not because colder water is less dense than warmer water.
Water is most dense at 4 C.

R
4C is the average energy. Below that it starts to crystallize because some molecules can be at freezing point.

#### Darien

##### Platinum Member
after thinking about the problem more, I've come to teh conclusion that a rubber band has to EXPAND when it's cooled.

Under tension, the rubber band will increase its length, and the entropy would decrease since the # of arrangements decreases as it becomes more 1-D. heating the rubber band -> increased entropy. the only way to do that is to become less like a linear chain. In other words, contract.

now to see where i screwed up in the math...

#### Darien

##### Platinum Member
bump. would like confirmation

#### thawolfman

##### Lifer
Bump for this guy since I have absolutely no idea wtf's going on in here! :Q

-Ben-