Review Problem. What is the required resistance of an...

Review Problem. What is the required resistance of an immersion heater that increases the temperature of $1.50 \mathrm{~kg}$ of water from $10.0^{\circ} \mathrm{C}$ to $50.0^{\circ} \mathrm{C}$ in $10.0 \mathrm{~min}$
while operating at $110 \mathrm{~V} ?$

Key Concepts

Energy-Power-Time Relationship

This principle states that energy is the product of power and time (E = P × t). It connects the rate at which energy is used or produced with the total energy delivered over a fixed period, making it critical for determining the needed power output in timed heating scenarios.

Specific Heat Capacity

This concept refers to the amount of heat energy required to raise the temperature of a unit mass of a substance by one degree Celsius. It is fundamental in determining the thermal energy needed for a given change in temperature, regardless of the material being heated.

Thermal Energy Calculation

Using the relationship Q = m × c × ?T, where Q is the heat energy, m is the mass, c is the specific heat capacity, and ?T is the temperature change, one can calculate the total energy needed for a heating process. This calculation is essential in connecting thermal physics with practical energy requirements.

Electrical Power and Resistance Relationship

In electrical systems, the power dissipated by a resistor can be expressed as P = V² / R, where V is the voltage applied and R is the resistance. This relationship is key in designing devices like heaters, as it links the electrical characteristics of a heating element to its ability to convert electrical energy into thermal energy efficiently.

Unit Conversions

Ensuring all units are consistent is vital when performing calculations that integrate thermal and electrical variables. Converting time (for example, minutes to seconds) and other units properly helps maintain accuracy in computations across the different physical domains.

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