What should be the resistance of a heating coil which will...

What should be the resistance of a heating coil which will be ased to raise the temperature of 500 g of water from $28^{\circ} \mathrm{C}$ to the boiling point in $2.0$ minutes, assuming that 25 percent of the heat is lost? The heater operates on a $110-\mathrm{V}$ line.

Key Concepts

Specific Heat Capacity

This concept pertains to the amount of energy required to raise the temperature of a unit mass of a substance by one degree Celsius. It is a fundamental property used in calculating the total energy needed to heat a material, which is critical when designing systems that involve thermal energy transfer.

Energy Transfer and Heat Loss Efficiency

In practical heating applications, not all the energy produced is used to heat the substance, as some is inevitably lost to the environment. Accounting for efficiency or percent heat loss is essential to determine the actual energy input required to achieve the desired temperature change in the system.

Electrical Power and Joule Heating

Electrical power in resistive heating is governed by the principle of Joule heating, which states that the power dissipated in a resistor is proportional to the square of the voltage across it divided by its resistance. This relationship is crucial when converting electrical energy into thermal energy in heating coil applications.

Resistance Calculation from Electrical Energy Requirements

Once the total energy requirement, adjusted for efficiency, and the duration over which heating must occur are known, engineering principles are applied to compute the resistance needed for the heating coil. This involves using the relationship between power, voltage, and resistance to ensure the system delivers sufficient energy within the specified time.

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