If the battery is for example 3.5mm x 14mm x 20mm and is 3.7V what is it's capacity?
How accurate can such calculation be?
How to calculate battery capacity from its size
batteriescapacity
Related Solutions
Your 75W fan required 220 Volts, it will not operate at typical battery voltages such as 12V.
A 75W fan operating (indirectly) from a 12V supply would draw 6.25 A not 0.34 A.
Even with a theoretical 100% efficient invertor, the current on the 12V side is greater than the current on the 220V side to deliver the same power across the system from battery to Fan.
Note that the reason that power is delivered through the grid at high voltage is to keep currents low. losses and cable sizes are proportional to (a function of) current. High V are used to keep currents low.
You convert 12V DC into 220 V AC using your inverter. Depending on capacity and utilisation the efficiency of an inverter might be the 80% you estimate or it may be worse - 50% Ref So your 6.25A may become 13A drawn from the 12V battery.
Therefore your 300 Ah battery-set might power a 75W fan for less than 24 hours.
Update: for 2 x nominal 12V SLA battery, the following diagram may clarify what is happening.
simulate this circuit – Schematic created using CircuitLab
Let's properly define what this capacity is that you're talking about.
It is the amount of (usable) energy you can extract from the battery of fuel cell.
Battery capacity is specified in Amp-hour where 1 Ah is 1 Ampere of current for 1 hour. For the energy you will also need the cell's voltage because only voltage times current gives you power. So a 3.7 V 1 Ah battery can supply 3.7 V * 1 A = 3.7 W for 1 hour or 3.7 WattHour (3.7 Whr). 3.7 W equals 3.7 Joule/second, 1 hour is 3600 seconds, so 3.7 * 3600 = 13320 Joules. That is the amount of energy you can extract from that battery !
You can do something similar with a fuel cell. I am unfamiliar with fuel cell specifications but I'm guessing it will have a specification for efficiency (how much of the energy in it's fuel it can extract) or amounts of power (in Watts) it can supply given a certain fuel consumption rate.
It all depends on what you know about the fuel cell and then you can do the calculation. It should be possible to end up at the amount of Joules you can extract from the cell, assuming you have the required data.
Best Answer
While you could use a "Energy density per volume" calculation, I think the safest bet would be to search for similar sized/priced/application batteries and make an estimate from there.
Since you know its 3.7V, I'll assume its Li-ion. From Wikipedia, we could say 250 to 620 W·h/L. Since your battery is roughly one milliliter, we can estimate from 0.25 to 0.62W.h, or 67mAh to 167mAh.
Now, we can double check that by looking for small Li-ion batteries on the web:
This one is a little bigger, offering 110mAh, while this other seems to be a bit smaller offering 40mAh.
From that I'd say the wikipedia numbers are a bit optimistic, because probably it takes into consideration the whole range of batteries (from the cheap ones we are looking at to others with super high density, etc..).
Next step is a guess, if you think this battery is new, good quality, from a good manufacturer, you can be optimistic. If its old, cheap and not taken much care for, then be a bit more pessimistic.
Anyway, its not a safe method at all, but should give a ball park. Ideally you would charge it and measure with different loads to be safe.