One rechargeable battery of mass 15.0 g delivers to a CD player an average current of 18.0 mA at 1.60 V for 2.40 h before the battery needs to be recharged. The recharger maintains a potential difference of 2.30 V across the battery and delivers a charging current of 13.5 mA for 4.20 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 $975 \mathrm{J} / \mathrm{kg}^{\circ} \mathrm{C},$ by how much will its temperature increase during the cycle?
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Given: Voltage (V) = 1.60 V Current (I) = 18.0 mA = 18.0 x 10^-3 A Time (T) = 2.40 hours Using the formula for energy delivered: \(E = V \times I \times T\) Substitute the given values: \(E = 1.60 \times 18.0 \times 10^{-3} \times 2.40 \times 3600\) (converting Show more…
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A rechargeable battery of mass $15.0 \mathrm{g}$ delivers an average current of $18.0 \mathrm{mA}$ to a portable DVD player at $1.60 \mathrm{V}$ for $2.40 \mathrm{h}$ before the battery must be recharged. The recharger maintains a potential difference of $2.30 \mathrm{V}$ across the battery and delivers a charging current of 13.5 mA for $4.20 \mathrm{h} .(\mathrm{a})$ 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? (c) If the battery is surrounded by ideal thermal insulation and has an effective specific heat of $975 \mathrm{J} / \mathrm{kg} \cdot^{\circ} \mathrm{C}$, by how much will its temperature increase during the cycle?
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