If a rubber band is stretched, the reversible work is given by [tex]\delta W = F \, dl[/tex], where [tex]F[/tex] is the tension on the band and [tex]l[/tex] is the length. Assume no [tex]pdV[/tex] term. Write down the differential form of thermodynamic potential [tex]\phi[/tex], which is a function of [tex]T[/tex] and [tex]l[/tex].

The differential form of the thermodynamic potential φ can be written as dφ = δQ + F.dl considering the given problem condition, where δQ is reversible heat, δW is reversible work, F is force and dl is the small displacement.

Explanation:

In the context of this problem, the differential form of the thermodynamic potential φ, can be expressed using the relation, dφ = δQ + δW , where δQ represents the reversible heat, and δW represents the reversible work done.

As per the assumption given in the question, we consider no pdV term, and hence, the reversible work is given by δW=F.dl, where F is the force and dl is the small displacement.

Therefore, in this case, the thermodynamic potential φ can be expressed as dφ = δQ + F.dl .

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