Help with proof of thermodynamics equation!

[ksingh1990]

1. The problem statement, all variables and given/known data
Suppose a thermodynamic system consists of a wire of length L under a tension T show that:
(dF/dL)=T
and
(dF/dT)=-S
(both are partial derivatives)


2. Relevant equations
F=U-TS
H=U+PV
G=U+PV-TS
dU=TdS-pdV
dF=-SdT-pdV
dH=TdS+Vdp
dG=-SdT+Vdp
dQ=TdS
dW=pdV


I'm getting confused with the T for temperature and T for tension. Please explain to me how to do this as I have no idea about where I should begin.
Thank You
1. The problem statement, all variables and given/known data



2. Relevant equations



3. The attempt at a solution

[Mapes]

How about modifying the differential equation dF=-S\,dT-P\,dV to incorporate work done by stretching the wire? Also, you can probably ignore P\,dV work in this problem.