- Duhem’s theorem is similar to the phase rule.
- It can be applied to closed systems in equilibrium where the system's intensive and extensive states are both fixed.
- Not only do intensive state phase rule variables decide the system's state, but extensive state variables such as phase masses or mole numbers are also needed.
- So, the total numbers of the variables are
- In addition to (Π - 1) N equations (as per the phase rule), a material balance equation can be written for each of the N chemical components.
- So, the total number of independent equations are
- The difference between the total number of variables and the total number of equations are
- Duhem’s Theorem Statement “For any closed system formed initially from given masses of prescribed chemical components, the equilibrium state is completely determined when any two independent variables are fixed.”
- As per Duhem’s theorem, we need to specify two independent variables. It may be intensive or extensive.
- The total number of intensive state variables can be found out by phase rule.
- For example: when F = 1, we can say one variable is intensive so another variable out of two must be extensive. And when F = 0, no intensive variable needs to specify both variables must be extensive.
2 + (N – 1) Π + Π = 2 + N Π
(Π – 1) N + N = ΠN
2 + N Π – Π N = 2
Important Unit Operations of Chemical Engineering
Laws of Thermodynamics
Fundamentals of Heat Transfer
Basic Concepts of Chemical Engineering Thermodynamics
The Phase Rule
Newtonian and Non-Newtonian Fluids
Hydrostatic Equilibrium