Help with proof of thermodynamics equation

In summary, the homework problem asks to show that the partial derivatives of F with respect to L and T are equal to T and -S, respectively, for a thermodynamic system consisting of a wire under tension. The relevant equations for this problem are F=U-TS and dF=-SdT-pdV. The confusion arises from the use of T for temperature and tension. To solve the problem, the differential equation can be modified to incorporate work done by stretching the wire, while ignoring PdV work.
  • #1
ksingh1990
1
0
1. Homework Statement
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. Homework 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
 
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  • #2
How about modifying the differential equation [itex]dF=-S\,dT-P\,dV[/itex] to incorporate work done by stretching the wire? Also, you can probably ignore [itex]P\,dV[/itex] work in this problem.
 

FAQ: Help with proof of thermodynamics equation

What is the equation for the first law of thermodynamics?

The first law of thermodynamics is represented by the equation ΔU = Q - W, where ΔU is the change in internal energy, Q is the heat added to the system, and W is the work done by the system.

How can the first law of thermodynamics be applied in real-life situations?

The first law of thermodynamics can be applied in various real-life situations, such as in the functioning of engines, power plants, and refrigerators. It can also be used to understand and analyze energy transfer and conversion in chemical reactions and biological processes.

3. What is the significance of the second law of thermodynamics?

The second law of thermodynamics states that the total entropy of a closed system always increases over time. This law is significant as it explains why some processes are irreversible and why energy cannot be completely converted into work.

4. How is the second law of thermodynamics represented mathematically?

The second law of thermodynamics is represented by the equation ΔS ≥ Q/T, where ΔS is the change in entropy, Q is the heat added to the system, and T is the temperature of the system.

5. Can the laws of thermodynamics be violated?

No, the laws of thermodynamics are fundamental principles that govern the behavior of energy in physical systems. They have been extensively tested and have been found to hold true in all known cases. Any apparent violations can be explained by considering the larger system or by taking into account external factors.

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