## Latent heat of vaporization

In order to know how much pure alcohol can be produced per minute or per hour by a 750 watt immersion heater we first need to know the rate at which the alcohol in the boiler is being vaporized and condensed in the still-head, i.e. the boil-up rate. When we know this volume we take 10 percent of it. That is the amount we can draw off and put into our martinis.

As discussed in the text, there are two methods of determining the rate of vaporization from the boiler — by direct measurement and by calculation. The calculation method is outlined below.

The rate at which liquid is vaporized is dependent upon two quantities; a) the energy input to the boiler, and b) the latent heat of vaporization of the liquid in the boiler (LHV). The LHV is the amount of energy required to convert a boiling liquid into vapour at the same temperature, and it is a surprisingly large quantity. The reason why energy is required to convert a boiling liquid into vapour without any rise in temperature is that molecules in a liquid are much more closely packed than in a vapour, and to convert one into the other the molecules must be wrenched away from the clutches of their fellows and push against the atmosphere. It takes energy to do this.

The energy required to vaporize water, i.e. the latent heat of vaporization (LHV), is 540 calories per gram. For ethyl alcohol the energy required is 220 calories per gram, the lower value being a reflection of its greater volatility. The composition we are involved with is 95% alcohol w/w. Simple arithmetic gives 236 calories per gram for the LHV of the 95% w/w alcohol azeotrope.

Why, you might ask, are we concerned with the energy required to vaporize 95% alcohol when we know very well that the contents of the boiler are mostly water and this water is being vaporized along with the alcohol? The explanation is this: 95% of the water vapour going up the column, car rying with it its latent heat of vaporization, is condensed in the column by the descending flow of liquid from the stillhead. The 5% water which does get through only does so because it is associated with ethyl alcohol in the azeotrope. When the 95% water condenses in the column it gives up its energy, this energy being known as the latent heat of condensation (LHC). It has the same value as the latent heat of vaporization. Therefore, the only energy escaping into the stillhead is the latent heat contained in the 95% alcohol and the 5% water. That's all there is in the stillhead and all that is being condensed by the cooling coil. Most of the water never gets there.

It is known that 860,000 calories/hour = 1 kilowatt. Therefore 860 calories/hour = one watt and 236 calories/hour = 0.27 watt

What this means is that 0.27 watts of electric power are required to vaporize 1 gram of a 95% alcohol/water mixture in one hour, so 750 watts would vaporize 2778 g/hr. or 46 g/minute. Ethanol having a S.G. of 0.8 the volumetric figure for the total reflux rate is 58 ml/minute.

When we measured the rate of reflux at total reflux with 750 watts input to the boiler we found a value of 45 ml per minute. This is less than the calculated value of 58 ml per minute because of heat loss due to imperfect insulation. This loss is equivalent to 168 watts.

If you cannot or do not wish to measure the rate of reflux yourself, you could use our figure of 45 ml. The insulation used for your boiler and column may be better or worse than ours, but is unlikely to differ very much, so you'd be pretty safe to use this figure of 45 ml.. This would mean that you could draw off 10% of this, or 4.5 ml per minute, as usable alcohol. This is particularly true since the reflux ratio of 10:1 is not critical anyway.

A footnote to this discussion is that the rate of reflux does not change during the course of a distillation, even though alcohol is steadily leaving the boiler and changing the composition and the boiling point of the liquid in the boiler. The composition of alcohol vapour in the stillhead remains constant from the time the heads are finished until the arrival of the tails, and that's all that matters; the composition of the liquid in the boiler is irrelevant.