- #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).