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. Show that:
a) The internal energy U is a function of temperature only
b) Adiabatic stretching of the band results in an increase in temperature (solved)
c) The band will contract if warmed while kept under constant tension
f = kT
(df/dt)L = k
The Attempt at a Solution
I think I need an equation of state for the band for part (a)
For part (b), adiabatic stretching means stretching with no heat going in or out of the band. To stretch it, the tension must be increased. f = kT:
f1/T1 = f2/T2
T2/T1 = f2/f1 If the band is stretched, f2/f1 is >1 so T2/T1 >1 therefore T2>T1. The temperature has increased.
For part c), I can write the total differential, then let df = 0 but that doesn't give much. Intuitively this makes sense, I just need to formalise it.