Quick: I'd have a good look at GP ReCyko cells as a good starting point
Some assumptions:
- For temperature >> zero C a lower reporting rate may be OK. Presumably the station could transmit say once per hour as a confidence check BUT drop into "fast" mode whenever a temperature drop threatened.
- Assume total TX cycle at 500 mW is 1 second per 10 minutes.
- 1s/10mins x 500 mW = 5/6 mW. Assume 1 milliWatt means draw. Adjust as required.
- Assume ~~10V pack for convenience --> 0.1 mA mean draw.
- 6 months ~= 4000 hours or ~400 mAh delivered capacity required.
- So worst case 6 months of late Autumn - Winter - Spring a 3 times over provision of battery capacity to allow for temperature effects requires about 1200 mAh. 4x = 1600 mAh. 5 x = 2000 mAh.
So AA cells of 1200 mAh in many chemistries would probably work (see below).
Primary cells are not a terrible idea. AA Alkalines at 2500+ mAh and a degradation factor of say 3x average would last about 2 years.
Solar recharging looks highly attractive. 1 mW mean power = 24 mW.hour / day. ie 1 hour of charging at say 50 mW would suffice to keep the battery always topped up. That's about a 1 square inch mono or poly crystalline solar panel exposed to
one "sunshine hour" of sunshine per day on average. As a guide, that would be more than adequate in NY NY in January (worst month) , and 3 square inches would work in Moscow in Russia in mid winter.
In all matters to do with batteries YMMV widely - experience is unfortunately the best guide as to how good claims are. Results can be very dependent on manufacturer. In many cases, if you don't have the volume to do your own investigations (and few do), choosing a reputable brand label which has been in the business for a substantial period and which is liable to have researched the product they sell and stand behind the results.
I would accept as likely to be approximately true, technical claims by Chinese makers BYD, BPI and GP (GoldPeak). Also mainstream labels such as Sanyo (make their own cells, usually very competent) etc. Most others I'd treat with far more care. Note that GP are so successful that there are Chinese clones of their products.
Note that for 6 months + lifetimes the self discharge rate of the battery used becomes relevant. NimH is very poor, NiCd is poor, lead acid are good and Lithium Ion and LiFePO4 are very good. Low Self Discharge (LSD) Nimh are very good. The latter are available as eg Sanyo Eneloop and GP ReCyko. Also now many more.
For general use the GP ReCyko are excellent. I have not yet found data on low temperature operation but I guesstimate that, based on other NimH data they'd be OK to say -20C at a sensible derating of their capacity - say 33% of nominal.
LiFePO4 are usually specified as operating to -20C. They will have substantial capacity loss at this temperature. Here's one manufacturers example. Reputable manufacturers are generally happy to provide detailed data to genuine inquirers.
Capacity loss
That graph is from Hi Power group which seems to be a typical Chinese manufacturer. All such information should be regarded as a starting point and "due diligence" is definitely required for anything regarding batteries.
GP rate their NimH batteries as operating to -20C. I have no data on this but its probably available. Here's a sample GPn1500 mAh NimH datasheet I'd expect lower capacity batteries within a given size range to have somewhat improved low temperature operation all else being equal. eg 1500 mAh AA better that 2500 mAh AA. But the increased initial capacity may cancel this out. (Larger capacity batteries squeeze in all possible active material at the expense of electrolyte volume etc).
You can get NimH and NiCd in special low temperature versions. Here are some examples from Lionik battery Co another typical looking Chinese manufacturer.
You will be able to get US branded and sold low-temperature batteries. These will almost invariably be Chinese made. Choosing a reputable US label gives you some confidence (or hope) that they have done the due diligence required to ensure that claims meet reality.
Here's a somewhat informal comparison of LiFePO4 with 4 other Lithium battery chemistries. Note that in 3 cases Tmin is given as -20C. Proves little but worth noting.
If you believe the battery manufacturer, and you're sure your circuit consumes 100mA, then the answer is:
2600mAh / 100mA = 26h
But you obviously need to verify your circuit's actual consumption. The above calculation should be considered an estimate.
My experience flying radio controlled planes have shown me that the estimate is actually quite good. Depending on the manufacturer it could even be conservative.
Modern RC batteries tend to understate the mAh numbers because hobbyists have started to depend on the simple calculations above to plan really long range flights. Also because reviewers started to compare battery performance on youtube. Generating more than the stated mAh when the battery is drained down to 0% (around 3.2V or 3.4V depending on opinion) makes the brand of battery very popular among RC pilots.
Non-branded or non-RC batteries however don't have this competitive pressure. So they may even over-rate the mAh numbers.
As for regulation, your circuit can take up to 5V and operate down to 2.5V. This is well within the battery operating voltage range. You don't need any regulator. You only need one if you plan on using 2-cell batteries (7.4V).
Best Answer
You can see from the comments that your only potential option is from the lithium chemistry. The lead acid is just way too heavy and probably too bulky as well.
265Wh/Kg is quoted for lithium. This is correct, but also more of an accepted 'potential' value and not necessarily what you will get given your specific needs. For example your need for a relatively high current might require a lithium battery that is constructed slightly differently giving you a lower capacity per kilogram.
Let's look at what you can get in the real world. The LiMn battery that powers the Nissan Leaf will handle your compressor. With a little rearrangement of the cells you could make it into a 12.6 volt 60 Ah battery that weighs exactly 12 lbs (5.5kg). It would give a nominal 684 Wh and can supply as high as 240 amps! Note that this lithium battery doesn't come close to the example given by Russel McMahon!
Depending on your compressor's duty cycle, this might work for the 10 hours, or it might only give you 3 hours. You will easily get the 100 cycles you asked for even if your depth of discharge is 90%. .
This battery could be purchased for about $160 or so.