A small dry battery of zinc and ammonium chloride weighing...

A small dry battery of zinc and ammonium chloride weighing 85 g will operate continuously through a $4-\Omega$ resistance for 450 min before its voltage falls below 0.75 V. The initial voltage is $1.60,$ and the effective voltage over the whole life of the battery is taken to be $1.00 .$ Theoretically, how many kilometers above the earth could this battery be raised by the energy delivered under these conditions?

Key Concepts

Gravitational Potential Energy

Gravitational potential energy is the energy required to raise an object to a certain height in a gravitational field, expressed as E = mgh. This concept is used to relate the electrical energy delivered by the battery to the mechanical work done in lifting a mass against gravity.

Unit Conversion and Dimensional Analysis

Accurate calculations in physics require consistent units. This includes converting time units (like minutes to seconds) and mass units (like grams to kilograms) to ensure that equations for energy and work are dimensionally consistent, leading to valid and comparable results.

Electrical Energy Calculation

Electrical energy can be calculated by multiplying the power delivered by the battery by the time of operation. Power in an electrical circuit is determined by the voltage across and the resistance of the load, often using relationships such as P = V²/R, which then provides the total energy output over the specified period.

Chemical Energy in Batteries

Batteries store energy in chemical form, which is then converted into electrical energy when the battery discharges. This concept involves understanding that the amount of energy available from a battery can be estimated from its voltage, capacity, and the duration over which it provides current.

Ohm's Law and Circuit Relationships

Ohm's Law describes the relationship between voltage, current, and resistance in an electrical circuit (V = IR). This fundamental principle is used in conjunction with power formulas to determine how much energy is delivered by a circuit when a known resistance is applied.

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