Ragone plot of an ideal battery

We are interested here in tracing the Ragone plot for an ideal battery (meaning no inductive effect is taken into account, no frequency-dependency of the values, no intrinsic nonlinearity of the component). The battery is assumed to preserrt a charge Q0 at the initial time and an internal resistance of value R. It is connected to a charge/discharge system with constant power P (see the diagram below). 

1) Trace the Ragone plot for this ideal battery, assuming there to be no leakage resistance Rf = on the diagram above). 

2) Then trace the plot in the case where the leakage resistance has a finite value 

1) Here the battery is considered with a constant voltage (independent of the charge), given by  

In order to identify the appropriate valne of/, we focns on the case where P 0. In this case, two possibilities can be envisaged /+ - Uq /R (which in practice corresponds to a short-circnited operation) and / 0 (which in practice corresponds to an open-circnit operation). Clearly, in the context of tracing the Ragone plot, only the second scenario here is of interest to ns, so / = /.  

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