How to find time constant of battery first order model with unknown capacitance?
Is this an assignment or homework?

Vem is the O/C voltage.   

R1 + R0 govern the voltage droop under load.
Vo = Vem - Iload.(R1 + R0). 

The Vo/c sags after a load is removed and then restores with time to Vem.
In fact, the action is more complex than this as Vem will drop over time as the battery is depleted - but this model does not show that. 

SO If
 - Vem drops to say Vl under load of Iload,
 - recovers instantly to Vr1 when load is removed
 - then recovers to Vem after time Tr 

then
Vload = Vem - (R0+R1) x Iload - rearrange to get R0 + R1. 

Vc = Vem-- Vr1. -> Calculate ratio of R0 to R1. 

Recovery time t = time constant or R0 and C. As T=RC.
Tr = R0.C -> calculate C