One rechargeable battery of mass 15.0 g delivers an average...

One rechargeable battery of mass 15.0 g delivers an average current of 18.0 $\mathrm{mA}$ to a compact disc player at 1.60 $\mathrm{V}$ for 2.40 $\mathrm{h}$ before the battery needs to be recharged. The recharger maintains a potential difference of 2.30 $\mathrm{V}$ across the battery and delivers a charging current of 13.5 $\mathrm{mA}$ for 4.20 $\mathrm{h}$ . (a) What is the efficiency of the battery as an energy storage device? (b) How much internal energy is produced in the battery during one charge-discharge cycle? (b) If the battery is surrounded by ideal thermal insulation and has an overall effective specific heat of $975 \mathrm{J} / \mathrm{kg} \cdot^{\circ} \mathrm{C},$ by how much will its temperature increase during the cycle?

Key Concepts

Specific Heat and Temperature Change

This concept entails the relationship between the amount of energy absorbed by a material and the resulting change in temperature, governed by its specific heat capacity. In the context of an insulated battery, the internal energy losses that are not converted to electrical energy lead to a measurable temperature increase, as determined by the formula ?T = Q/(mc).

Internal Energy Generation

Internal energy generation in a battery refers to the energy transformations and losses that occur within the battery during charge-discharge cycles. This encompasses chemical reactions, irreversible processes, and heat generation resulting from inefficiencies, which collectively account for the difference between the energy input and the useful energy output.

Electrical Energy Calculation

This concept involves determining the total energy delivered or absorbed in a circuit by multiplying the voltage across a component by the current flowing through it over a specific period of time. It is central when analyzing devices like batteries where the energy output during discharge and input during charging are calculated using the relationship E = VIt.

Battery Efficiency

Battery efficiency quantifies how effectively a battery converts stored chemical energy into electrical energy during discharge, and how much energy is lost during the charging process. It is calculated as the ratio of energy delivered during discharge to the energy consumed during charging, highlighting losses within the battery system.

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