ANS:D - all (a), (b) and (c)

The Fenske-Underwood equation used for calculating the minimum number of theoretical plates in a distillation column is valid for constant relative volatility. The Fenske-Underwood equation is a fundamental equation in distillation design and analysis. It is used to calculate the minimum number of theoretical plates required for a given separation, based on the relative volatility (𝛼α) of the components being separated. The equation is: 𝑁min=log⁡(𝛼min)log⁡(𝛼min−1𝑅min)Nmin​=log(Rmin​αmin​−1​)log(αmin​)​ Where:

• 𝑁minNmin​ is the minimum number of theoretical plates required.
• 𝛼minαmin​ is the minimum relative volatility required for the separation.
• 𝑅minRmin​ is the minimum reflux ratio required for the separation.

The Fenske-Underwood equation assumes constant relative volatility throughout the distillation process. Therefore, it is valid when the relative volatility remains constant during the operation of the distillation column. While constant molal overflow and total reflux are specific operating conditions that may affect the performance of a distillation column, the Fenske-Underwood equation itself is not directly tied to these conditions. Instead, it focuses on the fundamental concept of relative volatility in distillation separations.