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The "role" of enthalpy in electrochemical cells.

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Let's say that a battery (or electrochemical cell) has a total delta G value of -100 KJ and a total delta H value of -100 KJ. Does this mean that the battery will actually produce 100 KJ of heat AND 100 KJ of electricity when discharged (hypothetically)? If so, why don't batteries feel hot to the touch when in operation?
Assuming the battery is rechargable, shouldn't the battery get cold when being recharged since the reverse of the exothermic (-100 KJ) reaction is endothermic (+100 KJ)? If so, why does a battery being recharged not feel cold?

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"Does this mean that the battery will actually produce 100 KJ of heat AND 100 KJ of electricity when discharged (hypothetically)?"

No. 100 kJ is 100 kJ, whether it is released as 'heat' or 'electricity'. Actually, electricity is a means of transfering energy - devices in the circuitry will release heat, light, sound etc.

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