# Energy balance for convective drying vs. boiling. Energy required to transport water into dry air

OK, so. Huge debate with a co-worker. Help!

The fundamental question is which scenario requires more energy on a unit mass basis:

a) Boiling water in a closed vessel (typical boiler). b) Flowing 0% RH dry gas over a the surface of a pool of water to continuously remove water vapor (never reaching saturation vapor pressure).

My colleague believes that scenarios "a" and "b" will require the same amount of energy. I believe that scenario "a" will require significantly more heat. In scenario "b" we have a concentration gradient. Water should preferentially leave the surface of the pool in favor of the entering the dry air.

I would greatly appreciate your thoughts. Also, is there a simple way to prove this with thermodynamics? The math is rusty. I do have access to EES and am pretty familiar with it if that would provide a good way to go about it.

Thank you!

• If you have a large enough volume of 0% RH dry gas in contact with the pool and you just waited a long time couldn't you do it without any flow "for free" i.e. no energy input? – pentane Aug 26 '16 at 16:10
• Your question is not clear. What are the common starting and ending conditions? What is the goal of the processes a and b? – sammy gerbil Aug 26 '16 at 16:52
• What do you understand by a closed vessel? A pressure cooker, for example? And what Sammy said. – Gert Aug 26 '16 at 17:05
• @pentane, yes I could. – WTN Aug 26 '16 at 18:48
• @sammygerbil, assume I want to vaporize the same unit mass of water, starting at the same water temperature. – WTN Aug 26 '16 at 18:49

Thermodynamically, if the two processes have the same start and end conditions - eg converting 1 kg of water at room temperature (say $20^{\circ}C$) into vapour at $100^{\circ}C$ - they will use exactly the same amount of energy. If this were not the case, and these processes were reversible, you could run one process forwards and the other backwards in a continuous cycle, creating an unlimited amount of free energy.

On the face of it, blowing dry air over the water (forced evaporation) would require less energy - only enough to operate the fan and dry the air. But as Pentane points out, this would actually cause the water to cool. If it were isolated from the environment, some would evaporate but most would freeze. If it can draw heat from its surroundings, the energy lost via evaporation could be replaced, and the water could continue evaporating to dryness.

Alternatively, you could boil the water to dryness (free evaporation) in an open (not closed) vessel. This would use a lot more electrical energy to power the heating element. Much more than the fan uses. Most of this extra energy is being used to keep the water at the boiling temperature. Heat losses to the environment depend on the temperature difference between the water and the environment. Although the rate of evaporation would be higher than for the fan method, so too would the rate of heat loss to the environment.

But this is not a fair comparison. If the fan can make use of energy from the environment, why can't the boiling method also use a heat pump to take heat from the environment to raise the temperature of the water? This would reduce the electrical energy used by $2/3$. And why favour the fan method by allowing good thermal conduction with the environment? If the water tank were thermally insulated, this would further reduce heat losses, favouring the boiling method. The water in the fan method would now get very cold or freeze, taking much longer to evaporate, using more energy than the heat pump uses for boiling.

In the extreme, why not dispense with the fan and the heater, and let the water evaporate naturally, without the need for any man-made devices?

I think your argument has arisen because of not being clear about the conditions of the "experiment," and not "comparing like with like". Fair enough if one method makes use of ambient energy, but this needs to be explicit.

In a fair comparison, with exactly the same start and end conditions, exactly the same amount of energy would be required, either from the environment or from some man-made supply. However, depending on the conditions, either method could use less man-made energy and more from the environment.