system
Given the following post, respond as if you're commenting on Reddit:
human
How long will two 12v batteries heat a small room for?

I would like to set up a bike with a car alternator, put two 12v batteries in parallel, get an inverter and plug a low power heater into it to say, keep my (small)room temperature 22 Celsius in winter. How long would i have to cycle for to charge them?, to heat my room for how many hours? basically is it worth doing, or would i be exhausted for little result?
gpt
The voltage of the battery is only one piece of the puzzle and on its own doesn't say much about how much energy it contains. The second component is the amount of charge in the battery. This is often measured in Ampere-hour (short: Ah) or milli-Ampere-hour (mAh). 1 Ampere-hour is simply the amount of charge that allows a 1 Ampere current to flow for 1 hour.

The energy content of a battery can be calculated by multiplying the voltage with the charge content. The outcome is expressed in Watt-hour, Wh. 1 Wh is the amount of energy used in 1 hour with a power of 1 Watt. 1 Wh is equal to 3600 J (Joule).

So a 12 V battery with 10 Ah of charge (which through quick googling seems to be a decent amount for a rechargable 12 V batterypack) will be able to provide 120 Wh of energy (or 432 kilo-Joule (kJ)). What can you do with this? Well, a 60 W lightbulb uses 60 Wh over the course of 1 hour. So you could run a 60 W bulb for 2 hours.

Small electric heaters that are intended to heat an entire room (as opposed to those that just blow hot air at a single person) use between 1 and 2 kW of power. That means that you're 12 V, 10 Ah battery would be depleted in about 4 to 8 minutes. Twice that if you use two batteries. This is not counting any losses due to inefficiencies in power conversion (which will be turned into heat, so they're not actually losses when heating up the place is the goal).

Suppose you use a heater that is designed to only heat you as a person rather than the room. You can find these at around 500 W. The 12 V / 10 Ah pack could power this for about 15 minutes in the ideal scenario. How long would you have to cycle to charge it?

According to Wikipedia, the best bike dynamos will provide about 6 W of useful power output. Ignoring any losses while charging, this means that you need to bike for just 20 hours to charge up 120 Wh of battery capacity.

So 20 hours of biking for 15 minutes of heating. Not really worth it.

A somewhat related point of interest is that you have a more effective long term space heater available. You typically fuel it with various forms of biomatter (most models take plant and animal remains, though some shun the latter) and averaged over the day, this heater produces about 100 W of heat.

That's right. The average daily energy consumption of a human adult is somewhere around the 2000 KCal, which is 8.4 MJ. That boils down to around 100 W. Of course, in periods where you're active this'll be higher than in the passive moments. But even in passive moments it's a non-trivial amount. Which is why poorly ventilated rooms can heat up noticably when people stay in them for an extended period of time.

That means that you can still heat up your room by cycling, without having to mess around with batteries and space heaters. As long as you do the cycling inside your room. Your own heat production will heat the room much more than any battery-based solution ever could.

edit: Several people have correctly pointed out that a bike dynamo is meant for powering a small light while the bike still has to move. If you don't have to move, you can of course generate considerably more power. Ultimately though, you won't be able to power a very moderate space heater (1 kW) directly yourself with a 1:1 charge:use time ratio. Even a personal heater at 500 W will take an extremely good physical condition to reach 1:1 charge:use time.