It seems to me that the calculations in the original post are not quite right.

> 1F = 1V * 1 Coulomb.

The Farad is a Coulomb per Volt or Q/V not Q * V

This starting point inserts errors in the calculations that follow.  

For example:

> Thus 1F = 1V * 1 Amp Second.

The unit V * Amp * sec is equal to watts * sec =  energy in joules.  A Farad is 
not a joule of energy.

Also note that the voltage drops in a capacitor as you draw current from it, so 
you need some circuitry to keep the voltage up to keep your QRP rig happy.  As 
a result there is probably some practical level where the capacitor still has 
energy left, but it can not be effectively used any more.  (The rig would still 
work for a while as voltage dropped, but in the example given the voltage is 
considered constant at 12 Volts.)
A better approach to this calculation might be to start with the total energy 
stored in the 5000 F cap that was charged to 12 V.  The energy stored in a cap 
is:

Energy = (1/2) * C * (voltage squared)    where C is in Farads, V is in volts, 
and Energy is in Joules 

In the example that was used, the QRP rig takes a constant 12 volts dc at a 0.5 
amp.  This is 6 watts or 6 Joules per second.  If this constant power could be 
drawn from the capacitor until exhausted, then the time it would last would 
directly follow by dividing the initial energy in the cap by the rate of energy 
removal.  However, the added circuitry mentioned above between the cap and the 
rig would have losses, minimum useable cap voltage,  etc.
    73, Richard, KG4VOX
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