Why is it not possible to derive Cv from equation of state?

In summary: U/∂V)T. These quantities require more detailed microscopic information about the system. Therefore, there is a fundamental difference between the equation of state and other thermodynamic quantities, as the equation of state only provides a macroscopic description of the system. In summary, the equation of state and number of particles alone are not enough to determine all thermodynamic quantities such as Cv and (∂U/∂V)T. More detailed microscopic information is needed.
  • #1
Frank0
4
0
Assume you have no knowledge about the microscopic information, all you know about the system of pure material is it's equation of state and number of particles. Why can't we get Cv=(∂U/∂T)V from here(if this is wrong how do we solve it?)? Why can we obtained some other quantities just from equation of state(Cp-Cv, (∂U/∂V)T for example)? Is there any fundamental difference between these different types of thermodynamic quantities?
 
Physics news on Phys.org
  • #2
Frank0 said:
Assume you have no knowledge about the microscopic information, all you know about the system of pure material is it's equation of state and number of particles. Why can't we get Cv=(∂U/∂T)V from here(if this is wrong how do we solve it?)? Why can we obtained some other quantities just from equation of state(Cp-Cv, (∂U/∂V)T for example)? Is there any fundamental difference between these different types of thermodynamic quantities?
A simple equation of state would be: PV=nRT

You would be able to determine that Cp(T)-Cv(T) = R. But it is not enough to allow you to determine Cv or Cp. To determine Cp or Cv you first would need information about the degrees of freedom of the molecules (monatomic, diatomic, polyatomic). If it is not monatomic, one would also need to have experimental data as to how Cv and Cp varied with temperature.

AM
 

What is Cv?

Cv, also known as heat capacity at constant volume, is the amount of heat required to raise the temperature of a substance by 1 degree Celsius at constant volume.

What is an equation of state?

An equation of state is a mathematical relationship that describes the physical properties of a substance, such as pressure, temperature, and volume.

Why is it important to know Cv?

Knowing Cv is important in understanding the thermodynamic behavior of a substance and its ability to store or release heat energy.

Can Cv be derived from an equation of state?

No, Cv cannot be directly derived from an equation of state because it is a specific property that is dependent on the internal energy and molecular structure of a substance, which cannot be fully described by an equation of state.

What alternative methods can be used to determine Cv?

Cv can be experimentally measured using techniques such as calorimetry or by using thermodynamic tables that provide specific heat values for different substances at different temperatures.

Similar threads

I Partial derivative of wire tension relative to temperature, holding wire length constant.
    • Classical Physics
Replies
4
Views
617
A Deriving Non-linear acoustic wave models, equilibrium state assumption
    • Classical Physics
Replies
1
Views
594
A Conservation Laws from Continuity Equations in Fluid Flow
    • Classical Physics
Replies
2
Views
789
Equations of State in Modern Classical Physics (Thorne/Blandford)
    • Classical Physics
Replies
7
Views
1K
I Why is estimation of ##\frac{Pv}{RT}=1+BP+CP^2+...## interesting?
    • Classical Physics
Replies
2
Views
555
I Bernoull's Equation Derivation From Work - Energy Principle
    • Classical Physics
Replies
20
Views
2K
MHB Find Steady States for Equations: u, v and Get Help with Steady State Question
    • Calculus
Replies
1
Views
584
A Why are the Navier-Stokes equations inconsistent in this case?
    • Classical Physics
Replies
18
Views
994
I Bernoulli and Momentum Disconnect?
    • Classical Physics
Replies
4
Views
911
I Empirical temperature scales using different thermometers
    • Classical Physics
Replies
7
Views
836

Hot Threads

Recent Insights

Back
Top