Yep, caps in general are designed to store and release a charge quickly. The main difference in a supercap is that it charges quickly but discharges slowly and not capable of high currents due to internal resistance.
Things like motors, relays, solenoids require lots of current at startup, and relatively high currents throughout operation. So, a cap is well suited for help starting it up (hence why they are often used on motors) but not well suited for trying to power them long term.
You could experiment with PWM to prolong the use, but you have to start with a voltage higher than your motor requires. So, say 24V for your 12V motor. Then PWM max of 50% and you theoretically get twice the life out of a battery or whatever. A 12V or 24V solar panel will be fairly large though.
Your original question was how to turn the 2.5v from a supercap into 12V. You would use a voltage booster circuit (a special type of switching power supply) but it isn't that simple as you generally get less current capability out than you put in.
DROBNJAK:
Lets say one has this big super capacitor with 2.5V and 200-400F of charge. And you want to run 12V / 1A DC motor off that super cap. How is it done?
Charge is in coulombs, capacitance in farads (F). 2.5V and 400F would mean 1000C.
A boost converter is needed, and one which maintains the output voltage as the input voltage drops.
A capacitor stores energy equal to 0.5 C V^2, so 2.5V and 400F holds 1.25kJ, enough to supply 1A
at 12V for 100s assuming very efficient boost converter
A 400F supercap designed for high loads will probably handle 100A or more. Indeed a search
locates a WIMA SuperCapR 400F that handles 80A continuous, 600A pulse. Internal resistance
4 milliohms.
The main difference in a supercap is that it charges quickly but discharges slowly and not capable of high currents due to internal resistance.
Funny, I would think that it's internal resistance is reciprocal, in that if it can only discharge slowly then it should only be able to charge slowly as it's internal resistance dictates?
DROBNJAK:
Lets say one has this big super capacitor with 2.5V and 200-400F of charge. And you want to run 12V / 1A DC motor off that super cap. How is it done?
Charge is in coulombs, capacitance in farads (F). 2.5V and 400F would mean 1000C.
A boost converter is needed, and one which maintains the output voltage as the input voltage drops.
A capacitor stores energy equal to 0.5 C V^2, so 2.5V and 400F holds 1.25kJ, enough to supply 1A
at 12V for 100s assuming very efficient boost converter
As someone once told me right here, "wish I'd thought of that". jk Very efficient here meaning 100%. But I saw a 100% efficient solid state HF linear amplifier. The designer showed it to a crowd of hams and sure enough when powered by a car battery, it put out 600W @ just under 50A input. Nobody seemed to think a thing about it.
A 400F supercap designed for high loads will probably handle 100A or more. Indeed a search
locates a WIMA SuperCapR 400F that handles 80A continuous, 600A pulse. Internal resistance
4 milliohms.
Man they go all the way up to 3000F in the line with a 3000A discharge rate. I'd like to have a few of those. Wonder if they're regulated by an gov agency like DHS.
The ultra capacitor discharges fairly slowly. I have a demo here of running an Arduino from two of them together (giving just under 5V) and it ran for hours, doing a "lots of LEDs" demo which would have consumed a fair amount of current:
7 hours later it was a bit dodgy, but with a suitable step-up converter you could probably extract those last joules:
Very efficient here meaning 100%. But I saw a 100% efficient solid state HF linear amplifier. The designer showed it to a crowd of hams and sure enough when powered by a car battery, it put out 600W @ just under 50A input. Nobody seemed to think a thing about it. 