Consider a stretched elastic string. Then conducting a thermodynamic analysis of the elastic string. The approach is very similar to that used for $(P, V, T)$ systems, with the pressure and volume state variables replaced, respectively, by the string's tension J and its length L $(J,L,T)$.
The thermodynamic work can be given as $\delta W=-PdV$ for a $(P,V,T)$ system, analogous to this the work done on stretching an elastic string can be given as $\delta W=+JdL$
What assumptions would one make in both systems to arrive at the corresponding work equations above?
For the former case, I thought about the assumptions made when considering an ideal gas, such as:
- Gas molecules obey newtonian mechanics.
- Volume occupied by each molecule is considered negligible compared to the volume occupied by the entire gas. (i.e. point like gas atoms)
- Collisions are elastic.
- There exists no forces between the atoms/molecules constituting the ideal gas. (Except during collisions)
However I have no idea if this is helpful or not and if it is, how I can relate the following information to the latter system.