Batteries can work down to about -20 °C, but at the -50 °C where the payload will be, the chemical reaction that makes the battery work will slow sufficiently to render the battery useless. Lithium 9V batteries are proven to be reliable and safe in near space conditions as well as Lithium-Polymer (LiPo) rechargeable batteries. The problem with LiPo batteries is that they get complicated to care for with charging and other considerations. Some additional information is available on different types of batteries and their effectiveness, etc., but through extensive research this topic remains fraught with ambiguity. Do not use Lithium-ion (Li-ion) batteries because they do not get along well with the conditions of near space.
Batteries connected in series will have a voltage that is the sum of each individual battery’s voltage, while batteries added in parallel will keep the voltage the same as one battery on its own but combine to give additional charge. Adding a thousand batteries in series would create a scary amount of voltage, ready to destroy lots of things, while a thousand batteries in parallel could safely power a tiny electronic device for a very, very long time. If you have a device that will run off of, for example, a 9V battery but not for a long enough time, simply adding batteries in parallel will get you there.
The capacity of a battery is usually listed in milliamp-hours (mAh), which means that the total number of milliamp-hours divided by either (1) hours or (2) (milli)amperes will give you the other of the two values. The total available power can vary slightly based on the sustained current (higher current leads to lower total output) but this difference is relatively small. Below, Q is charge in coulombs, A is current in amperes (amps), and t is time in (in this case) hours.
To calculate the current of some element of your system you can use Ohm’s law, where V is voltage in volts, I is current in amps, and R is resistance in Ohms.
These calculations and others can be taken much further but that is left to the reader because there are already many resources available on this topic.
The battery chemical reaction will produce some of its own heat. It might be possible to insulate the battery and capitalize on this internal source of heat, but otherwise the batteries will need an external heat source, such as a heater block or an antenna (which is almost the same thing as a heater but much more useful!). This is a topic ripe for investigation and engineering modeling in the HAB community.
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