# How does a transfer of chemical potential energy occur in a circuit?

I am aware that simple DC circuits use a battery which is connected to several elements. In the case that the element is a resistor, I read that the circuit as a whole is an isolated system for energy and that the chemical potential energy in the battery is converted into internal energy of the resistor ( which appears as increased vibrational motion of the atoms of the resistor), essentially: $$∆U_{chem} = -∆E_{int}$$

My question is what exactly constitutes chemical potential energy in a battery? By definition, a potential energy exists between two particles / sub-systems that interact by means of a conservative force. The only conservative interaction I could think of was between free electrons as a product of redox reactions ( like in the Daniel cell ), but this constitutes to electrical potential energy, so I was unsure.

Secondly I was wondering how this energy was transferred over to the resistor. If I consider the resistor to be the system alone, the non-isolated system for energy would lead to an equation that I believe is: $$T_{ET} = ∆E_{int}$$ where $$T_{ET}$$ represents transfer variable referring to electrical transmission. I am unsure of what this means, but deduced that this would be the most sensible as the other transfer variables were either Work, Heat, Matter Transfer, Electromagnetic Radiation or Mechanical Waves.

Could someone please tell me how the transfer variable for Electrical transmission would work? (if my analysis is right?)