Answer
The electric potential across the battery is $~~0.10~V$
Work Step by Step
The rate at which energy is transferred to thermal energy is the slope of the energy versus time graph.
We can find the slope:
$slope = \frac{\Delta E}{\Delta t} = \frac{2.00~mJ}{4.0~s} = 0.50~mJ/s$
Note that this value is equal to the power.
We can find the electric potential across the battery:
$Power = \frac{V^2}{R}$
$V^2 = P~R$
$V = \sqrt{P~R}$
$V = \sqrt{(0.50~mJ/s)(20~\Omega)}$
$V = 0.10~V$
The electric potential across the battery is $~~0.10~V$
