The thing is, it doesn't have to be. The energy released by mixing salt into water is small, around 3.9kJ/mol.
Molar mass of salt is 58g/mol, and the average sea water salinity is around 3.6%
So a cubic meter of sea water will have 1000*0.036/0.058=620 moles of salt, and it'll require 2.4MJ of energy to remove the salt in a perfect desalinator.
In more common units, 2.4MJ is about 0.75 kWh. Around here electricity is ~10 cents per kWh, so the absolutely lowest price of one cubic meter of desalinated water would be around 8 cents.
> desalinating 35 g L–1 seawater at 50% water recovery has a theoretical minimum energy requirement of 1.1 kWh m–3 and a practical minimum of 1.6 kWh m–3.
SOTA is apparently ~3.7 kWh m-3. That's not a huge factor
> cubic meter of sea water will have 1000*0.036/0.058=620 moles of salt, and it'll require 2.4MJ of energy to remove the salt in a perfect desalinator. In more common units, 2.4MJ is about 0.75 kWh.
> A thousand liters takes about 3kwh.
So, if those numbers are right, desalination is currently at about 25% of theoretical energy efficiency. Is that correct?
Correct me if I am wrong as I am not a physicist. I see a point that is important to consider, that you have potentially overlooked. First, you assume that dissolution of salt is a completely reversible thermodynamic process, which is fine. But considering it a reversible process, in order to reverse the process we need to do a certain amount of work which you have calculated. In order to do work we need an engine. The most efficient possible engine is a Carnot engine. It is known that a Carnot engine can never be 100% efficient (unless we can achieve infinite or zero temperature). Given that you calculated the amount of work needed to reverse the process, you still need to bound the efficiency by the efficiency of a Carnot engine. Alternatively you need to factor in the efficiency of a Carnot engine to get the minimum required energy input.
You are correct. Although technically, dissolution is not a reversible process. That's why you need to input energy to reverse it.
Carnot cycle, technically, doesn't apply to all energy sources directly.
For example, solar panels have their "hot side" at around 6000K, so Carnot efficiency would be close to 100%. Real solar panels have other limiting factors, and I believe the absolute achievable theoretical maximum is around 80%.
On the other side of the spectrum, wind turbines have very lousy Carnot efficiency because they're exploiting a temperature difference of just a few degrees. However, the "Carnot tax" is not paid by us directly, so we don't really care about it.
According to the paper [1] he talks about in the video, the theoretical limit is a function of %salt removed and %waste-water.
For 90% salt removal with 50% waste-water, they say the limit is 1.09kWh per cubic meter (3.924 MJ)
NB: It is not 100% clear to me if the result is independent of the type of technology, but they do claim:
> We first derive the general expression of the thermodynamic minimum energy of separation determined by the Gibbs free energy, which is independent of the method of desalination
Molar mass of salt is 58g/mol, and the average sea water salinity is around 3.6%
So a cubic meter of sea water will have 1000*0.036/0.058=620 moles of salt, and it'll require 2.4MJ of energy to remove the salt in a perfect desalinator.
In more common units, 2.4MJ is about 0.75 kWh. Around here electricity is ~10 cents per kWh, so the absolutely lowest price of one cubic meter of desalinated water would be around 8 cents.