Steady-State Multiplicity of CSTR

The dimensionless steady-state equations of mass and energy balance for a CSTR are reproduced here  

For the nondimensionalization, the reader is referred to Section 2.7. From the physical arguments, the dimensionless concentration u is bounded between 0 and 1, i.e., 0 m 1. The relationship between the dimensionless concentration u and dimensionless temperature v can be obtained as 

Thus substitution of Equation (2.272) into Equation (2.271) yields 

If the condition in Equation (2.275) is violated, then uniqueness is assured if and only if 

---