- #1
Toby_phys
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Homework Statement
For a stretched rubber band, it is observed experimentally that the tension ##f## is proportional to the temperature ##T## if the length ##L## is held constant. Prove that:
(b) adiabatic stretching of the band results in an increase in temperature;
(c) the band will contract if warmed while kept under constant tension.
Homework Equations
the first law:
$$
dU=Tds+fdL=C_L dT
$$
$$
f=\left (\frac{\partial f}{\partial T}\right )_L T
$$
$$
\left (\frac{\partial L}{\partial f}\right )_T>0
$$
The Attempt at a Solution
(b)[/B]
For an adiabatic process, entropy doesn't increase and so:
$$
dU=fdL=C_LdT
$$
The force is always positive and so temperature is positively increased by length.
This feels too simple so i doubt I am correct. I have no idea for part (c).