A circuit consists of a single closed loop containing an ideal battery of electromotive force \(\mathcal{E}_1\), a rechargeable ideal battery of electromotive force \(\mathcal{E}_2\) (where \(\mathcal{E}_1 > \mathcal{E}_2\)), and a resistor of resistance \(R\). The two batteries are oriented in opposition such that their positive terminals face each other along the top wire, resulting in a steady clockwise current \(I\) through the loop.

Which of the following statements correctly identifies the rate at which battery 1 converts chemical energy into electrical energy and provides a valid justification based on the conservation of energy?