A capacitor of  $5\mu F$ is charged to a potential of 100 V. Now, this charged capacitor is connected to a battery of 100 V with the positive terminal of the battery connected to the negative plate of the capacitor. For the given situation, mark the correct statements.

Initial condition just after the connection of battery:

Condition after a long time: It means battery supplies $1000\mu C$ charge from its positive terminal and an equal and opposite charge enters from its negative terminal, i.e.,
charge flow through battery is $1000\mu C$. Work done by the battery is 

$W_{battery}=100V\times {10}^3\mu C=0.1J$

From energy conservation law $U_i+W_{battery}=U_f+\Delta H$

$U_i=U_{f}so\Delta H=0.1J$