Process Equipment and Plant Design
Smoker's equation for the calculation of number of equilibrium stages in a continuous binary distillation column is used, when the

Relative volatility is close to one (e.g., separation of close boiling isomers)
Feed is not at its bubble point
Number of equilibrium stages in only stripping section is to be calculated
Number of equilibrium stages required is likely to be very small

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Process Equipment and Plant Design
In the case of a shell and tube heat exchanger, the logarithmic mean temperature difference

Is always more than arithmetic mean value and the geometric mean value
Is always less than arithmetic mean value, but more than geometric mean value
May be either more or less than geometric mean and arithmetic mean value depending upon whether the flow of stream is co-current or counter-current
Is always less than arithmetic average value

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