A 12.0-V emf automobile battery has a terminal voltage of 16.0 V when being charged by a current

step 1 For this question we have a 12 volt automobile battery. You are given that as it charges by a cu

A 12.0-V emf automobile battery has a terminal voltage of...

A 12.0-V emf automobile battery has a terminal voltage of $16.0 \mathrm{V}$ when being charged by a current of 10.0 A. (a) What is the battery's internal resistance? (b) What power is dissipated inside the battery? (c) At what rate (in $^{\circ} \mathrm{C} / \mathrm{min}$ ) will its temperature increase if its mass is $20.0 \mathrm{kg}$ and it has a specific heat of $0.300 \mathrm{kcal} / \mathrm{kg} \cdot^{\circ} \mathrm{C},$ assuming no heat escapes?

Key Concepts

Specific Heat Capacity and Temperature Change

Specific heat capacity is a material property that indicates how much energy is required to raise the temperature of a unit mass by one degree. This concept is essential when calculating how the dissipated power (converted to heat) will affect the temperature of the battery, linking energy input to a resulting change in temperature under the assumption of no heat loss.

Power Dissipation (Joule Heating)

Power dissipation in the context of internal resistance refers to the conversion of electrical energy into thermal energy within the battery. This loss, calculated by the product of the square of the current and the resistance (I²R), represents the heat generated internally, which can impact the battery's performance and temperature.

Terminal Voltage and Electromotive Force (EMF)

Terminal voltage is the measurable voltage across the battery's terminals when it is under load, and it may differ from the EMF. The difference arises due to the voltage drop associated with the battery's internal resistance, particularly during charging or discharging, where the internal resistance affects the net output voltage.

Battery Internal Resistance

This concept describes the inherent resistance inside a battery that causes a voltage drop (or rise during charging) when current flows. It is crucial for understanding how the internal components contribute to the overall performance and efficiency of energy delivery, influencing the terminal voltage compared to the electromotive force (EMF) of the battery.

Ohm's Law and Voltage Drops

Ohm's Law connects voltage, current, and resistance, offering a simple relationship to calculate the voltage drop across the internal resistance. This principle is used to determine the internal resistance by relating the difference between the applied terminal voltage and the battery’s nominal EMF to the charging current.

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