The Ideal Column Thermodynamic Analysis

As stated earlier, the separation of mixtures into their constituents requires energy. In distillation, this energy is supplied as heat. To this end, it is useful to recall that Carnot (see Chapter 3 for details) showed that the maximum amount of work that can be extracted from a heat source Q at T T0 with respect to the surroundings at T0 is given by 

It is straightforward to show that if heat is available at temperature levels Th and Tu the maximum amount of work that can be extracted from the former temperature level is = Q[l-(T0)/(Th)], whereas W0 x = Q[1-(T0)/(T,)] is the maximum amount of work for the latter. From this, it can be shown that if heat flows spontaneously from a temperature level Th to a temperature level Tl (with Th T, T0), the amount of available work that has been lost is given by 

Another useful equation is the Clausius-Clapeyron equation. It states that, provided the ideal gas law holds and the enthalpy of vaporization, Aft, is independent of T (which is a reasonable assumption for a small temperature range), the slope of the vapor pressure curve is given by 

Consider two very similar components, propylene [1] and propane [3], with close boiling points. The ideal relative volatility is now defined as 

From Equations 10.5 and 10.6, it follows that over the temperature range of distillation 

---