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# Quick thermodynamics question watch

1. I need to show that adiabatic stretching of a rubber band causes an increase in temperature.

I've managed to reduce the 1st Law of Thermodynamics to dU=kLdL.

k,L and dL are all positive so dU is positive - the total internal energy increases.

But does this immediately imply that the temperature also increases?

Any help would be appreciated.
Thanks.
2. I see no temperature term in there , so I don't think it's implied... but the spec. enthalpy would increase? (h = u + RT, for an ideal gas, IIRC)
3. (Original post by + polarity -)
I see no temperature term in there , so I don't think it's implied... but the enthalpy would increase? (h = u + RT, IIRC)
It's adiabatic so the entropy is constant => dS = 0
So, TdS = 0 and the temperature term disappears
4. Doesn't adiabatic mean there is no heat transfer? So the Q in the NFEE = 0?

I am .
5. Well dQ=TdS so if dQ is zero, then dS must also be zero.
Either way, you're left with dU=dW=fdL=kLdL.
6. Ah, yes.

So the temperature shouldn't change. I think.
7. I thought it must, but then could the internal energy not be in the form of elastic strain energy rather than thermal?
8. (Original post by ryanwilk)
I thought it must, but then could the internal energy not be in the form of elastic strain energy rather than thermal?
I think this is what happens.
9. (Original post by + polarity -)
I think this is what happens.
Oh, and then the strain energy is converted to thermal energy or something?
10. (Original post by ryanwilk)
Oh, and then the strain energy is converted to thermal energy or something?
Well you do work on the rubber band to change its length, and this changes the internal energy. Since there is no heat transfer, there is no temperature change.
11. (Original post by + polarity -)
Well you do work on the rubber band to change its length, and this changes the internal energy. Since there is no heat transfer, there is no temperature change.
but the question asks me to show that adiabatic stretching of a rubber band does increase the temperature...
12. (Original post by ryanwilk)
but the question asks me to show that adiabatic stretching of a rubber band does increase the temperature...
Okay.

I'm sorry! I can't do it!
13. Maybe the internal energy is in the form of both thermal and strain energy, I mean there's always some heat loss, right?
14. The internal energy in a solid is roughly half kinetic and half potential. If you increase the internal energy adiabatically (let no heat leave) then the temperature will rise because you are increasing the kinetic energy of the molecules. (As well as potential)
15. Thank you!

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