Find the Canonical Equation for the Dieterici Equation of State

In summary, the conversation discusses the Canonical Equation of State, which is used to describe the relationship between energy, entropy, and volume in a gas. The author of Elements of Gasdynamics presents an equation for a perfect gas, using enthalpy as a variable. The conversation then moves on to discussing the Canonical Equation of State for E(V,S) in relation to Dieterici's equation of state. However, the speaker mentions having trouble integrating the equation for use in the ds=Q/T formula. They then ask for suggestions on how to solve this problem. The website cisco may be the source of this conversation.
  • #1
Chetty
32
3
Homework Statement
Find the Thermodynamic Canonical Equation of State for the Dieterici Equation of State
Relevant Equations
P=(RT/(v-Beta))*exp(-alpha/(RTv)
In Elements of Gasdynamics the author describes what he calls The Canonical Equation of State where (∂E∂S)v=T and (∂E∂V)s=−P He does a simple one for a perfect gas and uses the enthalpy(T,V) for the Canonical Equation of state. Now he asks to find the Canonical Equation of State for E(V,S) corresponding to Dieterici's equation of state.​

I tried using this in the pdv term but could not integrate it for insertion in the ds=Q/T equation. Any ideas?
 
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  • #2
It appears that this response is referring to another source. Is that at the listed website cisco?
 

1. What is the Dieterici equation of state?

The Dieterici equation of state is a mathematical model used to describe the behavior of gases at high pressures and low temperatures. It is named after the Italian physicist Ulisse Dieterici, who first proposed it in 1888.

2. What is the significance of finding the canonical equation for the Dieterici equation of state?

The canonical equation for the Dieterici equation of state allows us to express the relationship between pressure, volume, and temperature in a simplified and standardized form. This makes it easier to analyze and compare the behavior of different gases under varying conditions.

3. How is the canonical equation for the Dieterici equation of state derived?

The canonical equation for the Dieterici equation of state is derived by applying the principles of thermodynamics and statistical mechanics to the original Dieterici equation. This involves manipulating the equation and solving for the variables to obtain a standardized form.

4. What are the advantages of using the Dieterici equation of state?

The Dieterici equation of state has several advantages, including its ability to accurately describe the behavior of real gases at high pressures and low temperatures. It also takes into account the attractive forces between gas molecules, making it more accurate than simpler equations of state.

5. Are there any limitations to the Dieterici equation of state?

Like any mathematical model, the Dieterici equation of state has its limitations. It may not accurately predict the behavior of gases at extreme temperatures or pressures, and it may not be suitable for all types of gases. Additionally, it does not take into account the effects of intermolecular interactions such as dipole-dipole forces.

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