Adiabatic Stretching of a Rubber Band and the First Law of Thermodynamics

In summary, adiabatic stretching of a rubber band results in an increase in temperature due to the positive values of k, L, and dL in the first law of thermodynamics equation. This can be further demonstrated using differential identities and Maxwell relations, showing that the partial derivatives of entropy, length, and force with respect to temperature are all positive for an elastomer.
  • #1
ryanwilk
57
0
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.
 
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  • #2
(I've basically done:
dU = dQ + dW
dQ = TdS and dW=-PdV+fdL
=> dU = TdS-PdV+fdl
Assume constant volume => dV=0
f=kL
=> dU = TdS+fdl
S is constant in an adiabatic process so dS=0
=> dU = kLdL)
 
  • #3
I'd start with [itex](\partial T/\partial L)_S[/itex] and start applying differential identities, Maxwell relations, etc., to get it in terms of derivatives whose sign you know.

For example, are [itex](\partial S/\partial T)_L[/itex], [itex](\partial L/\partial T)_F[/itex], [itex](\partial L/\partial F)_T[/itex] positive or negative for an elastomer?
 

FAQ: Adiabatic Stretching of a Rubber Band and the First Law of Thermodynamics

1. What is thermodynamics?

Thermodynamics is the branch of physics that deals with the study of heat, energy, and work, and their relationship to each other and to physical systems.

2. How does thermodynamics relate to everyday life?

Thermodynamics is involved in many everyday processes, such as cooking, refrigeration, and electricity generation. It helps us understand how energy is transferred and transformed in these processes, and how we can optimize them for efficiency.

3. What are the laws of thermodynamics?

The laws of thermodynamics are fundamental principles that govern the behavior of energy and its transformation in physical systems. They include the first law, which states that energy cannot be created or destroyed, only transferred or converted, and the second law, which states that the total entropy of a closed system will always increase over time.

4. What is the difference between heat and temperature in thermodynamics?

Heat is a form of energy that is transferred between two objects due to a temperature difference. Temperature, on the other hand, is a measure of the average kinetic energy of the particles in a substance. In thermodynamics, heat and temperature are related, but they are not the same thing.

5. How is thermodynamics applied in engineering?

Thermodynamics is essential in engineering, as it helps us understand and design systems that involve energy transfer and transformation. This includes designing engines, power plants, and other devices that use energy to do work. Thermodynamics also plays a crucial role in materials science and chemical engineering.

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