University thermodynamics fundamental equation/identity derivation.

In summary, the conversation discusses the possibility of deriving a fundamental identity without using entropy. The equation in question is purely thermal and not related to entropy or statistical mechanics. However, the key to the derivation involves an identity that includes entropy. The other person expresses confusion about leaving out entropy, as it is a fundamental quantity in thermodynamics. They also point out a mistake in the last equation. The original person clarifies that they are wondering if the first equation can be derived using only P, T, and V without using the second law, which defines entropy as a "state" function.
  • #1
kntsy
82
0
Hi, how can i derive this fundamental identity "without using entropy"?
[tex]\left(\frac {\partial U}{\partial V}\right)_T = T\left(\frac {\partial P}{\partial T}\right)_V - P[/tex]

I believe the above equation is purely thermal and has nothing to do with entropy and statistical mechanics but unfortunately the below identity is the key to this derivation:

[tex]\left(\frac {\partial P}{\partial T}\right)_V = \left(\frac {\partial S}{\partial V}\right)_T[/tex]

of course:

[tex]dU=TdS-PdV[/tex]
 
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  • #2
What do you mean "without using entropy"? what do you mean by "purely thermal"?
Entropy is a fundamental quantity of thermodynamics. I don't see why you should want to leave it out of the game.

Btw. your last equation is wrong. (At least compared to the sign convention you use in the first two formulas, then the last one should be different.)
 
  • #3
Thaakisfox said:
What do you mean "without using entropy"? what do you mean by "purely thermal"?
Entropy is a fundamental quantity of thermodynamics. I don't see why you should want to leave it out of the game.

Btw. your last equation is wrong. (At least compared to the sign convention you use in the first two formulas, then the last one should be different.)

sorry for the mistakes. In other words, can we derive the first equation just using P,T,V; without using 2nd law(which defines entropy and shows that it is a "state" function)?
 

1. What is the fundamental equation/identity in university thermodynamics?

The fundamental equation/identity in university thermodynamics is the first law of thermodynamics, which states that energy cannot be created or destroyed, only transferred or converted from one form to another.

2. How is the fundamental equation/identity derived in university thermodynamics?

The fundamental equation/identity is derived using the principles of energy conservation and the definition of internal energy. It can also be derived using the laws of thermodynamics and the concept of entropy.

3. What does the fundamental equation/identity tell us about thermodynamic systems?

The fundamental equation/identity tells us that the internal energy of a thermodynamic system is a function of its state variables, such as temperature, pressure, and volume. It also shows the relationship between heat, work, and internal energy in a system.

4. How is the fundamental equation/identity used in thermodynamic calculations?

The fundamental equation/identity is used to calculate the changes in internal energy, heat, and work in a thermodynamic process. It can also be used to determine the equilibrium state of a system and to analyze the efficiency of heat engines.

5. Are there any limitations or exceptions to the fundamental equation/identity in university thermodynamics?

The fundamental equation/identity is a general law that applies to all thermodynamic systems. However, it may not be applicable to systems that involve extreme conditions, such as extremely high pressures or temperatures. It also does not take into account any energy losses due to friction or other inefficiencies in a process.

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