# Physicality of claims regarding AC ice energy storage units

Many of us may remember the problems from thermodynamics where we had to determine if a pretend air conditioning unit supplier's claims violated the 2nd law. I want to pose a similar question regarding a new "green" Air Conditioning (AC) technology.

An ice energy storage unit for AC works by making ice during the night and using the latent heat (mostly) to cool the building during the day. The major motive for doing this is to move the energy demand from the peak energy use times to the low-demand times at night when it is cheaper. The cost of electricity is not relevant to this question. The claims of a vendor of this technology, Ice Bear Energy Storage System, include the following:

Bottom line: The Ice Bear system reduces total net energy consumption for most buildings under virtually all operating conditions and installations.

Question: Is this claim physically plausible, given reasonable assumptions about climate? There are some example cities below, I imagine that considering an average location or just the extremes would be sufficient.

Here are a few things to note, but these are certainly not comprehensive. Creativity may be important for identifying all the factors at play.

• The temperature of ice is $0^{\circ} C$ ($32^{\circ} F$)
• Room temperature is $22.2^{\circ} C$ ($72^{\circ} F$)
• The outside ambient temperature is lower at night than during the day. Exactly how much depends on the location and humidity particularly. Locations mentioned on their website include Glendale, CA; Howell, NJ; Las Vegas, NV; Fort Collins, CO; Orange County, CA; and Redding, CA.
• The ice storage duration is 6 hours and since these are multiple MW products, I'll say it's fair to assume almost perfect insulation unless someone wants to challenge this.
• You can obtain useful work while exchanging the heat from the office building to the ice. I believe this would be important considering the wording of "total net energy consumption".

# Temperatures

I have looked up the temperatures for most of the mentioned cities. For some I couldn't get data for I used a nearby city instead.

• (City/State) (night-day difference) (seasonal difference) (hottest month high)
• Redding CA, 27.4, 44, 99
• Las Vegas NV, 26.5, 48, 104
• Denver CO, 27.8, 45, 88
• Lakehurts NJ, 27.8, 45, 88
• Santa Anna CA, 20.5, 18, 83

These seem to be fairly consistent for the night-day difference in particular. I hope that simplifies the problem. It seems clear that running at night "buys" you about 27.5 degrees F. Now, the absolute temperatures as well as the seasonal variation will affect the efficiency, but to a much smaller degree.

My conflict: Can a $27.5$ degree difference really make up for a $72-32=40$ degree penalty on the thermal cycle? Really? It's not a trivial problem, but I am skeptical. I will certainly send them an email letting them know they violated the 2nd law depending on the outcome here.

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@Omega Since this is only a relative comparison, bad assumptions may still lead to the right conclusion. But you're right that AC systems have to cool to lower than air temperature, and it will still be present for the water/ice mix. For instance, the $\Delta T$ due to an imperfect heat exchanger (HX) might be 15-20 F for the conventional HX and 5 F for the water/ice HX. But when you transfer the heat from the ice to the building during the day, if you extract energy from that cycle you are penalized by the same 15-20 F (same air circ system). Hope this makes sense. –  Alan Rominger Jul 12 '11 at 15:06