Current i is being driven through a cell of emf $\epsilon$ and internal resistance r, as shown 

a) The cell absorbs energy at the rate of $\epsilon$i 

b) The cell stores chemical energy at the rate of $\left(\mathrm{\epsilon i}-{\mathrm{i}}^2\mathrm{r}\right)$ 

c) The potential difference across the cell is $(\mathrm{\epsilon }+\mathrm{ir})$ 

d) Some heat is produced in the cell. 

For the given circuit, when i current is flow through the cell :

Rate of Energy absorbed by cell is

$\frac{\mathrm{dQ}}{\mathrm{dt}}=\mathrm{\epsilon i}$

Some of this energy is converted to heat at the internal resistance (r) :

Therefore, Rate of heat generated in the cell will be

$\frac{\mathrm{dH}}{\mathrm{dt}}={\mathrm{i}}^2\mathrm{r}$

Rest of the energy is stored in the cell at the rate of 

$\frac{\mathrm{dQ}}{\mathrm{dt}}-\frac{\mathrm{dH}}{\mathrm{dt}}=\mathrm{\epsilon i}-{\mathrm{i}}^2\mathrm{r}$

Potential difference across the cell will be 

$\mathrm{V}=\mathrm{\epsilon }+\mathrm{ir}$