(a) Estimate the maximum volume of an immersion heater in a...

(a) Estimate the maximum volume of an immersion heater in a single family house. (b) How much heat would be required to raise the temperature of that water from $20^{\circ} \mathrm{C}$ to a standard household hotwater temperature of $45^{\circ} \mathrm{C} ?$ (Water has a density of $1.00 \mathrm{~kg} / \mathrm{L}$ and a heat capacity of $4190 \mathrm{~J} / \mathrm{kg} \cdot \mathrm{K} .$ ) (c) Suppose the water should be fully heated in $1.5 \mathrm{~h}$. To what power output does this correspond? (d) If the element has a potential difference of $230 \mathrm{~V},$ what current is required? (e) What should be the resistance of the element?

Key Concepts

Estimation Techniques

This concept involves making reasonable assumptions and using approximations to determine the magnitude of physical quantities when exact values are not available. In this context, it applies to estimating the maximum volume of an immersion heater, where one uses typical sizes and specifications of household appliances to derive a ball?park figure.

Specific Heat Capacity

Specific heat capacity is the amount of energy required to raise the temperature of a unit mass of a substance by one degree. It is a central concept in calorimetry and thermodynamics, allowing the calculation of energy needed to change the temperature of a given mass of water by applying the formula Q = m × c × ?T.

Energy and Power Relationship

This concept connects the energy required for a process with the time over which that energy is supplied. Energy is calculated based on mass, specific heat, and temperature change, and when divided by the time interval, it provides the power needed. This relation underpins the design and analysis of devices that must deliver a certain amount of heat within a specified time frame.

Electrical Power for Resistive Heating

Electrical power in resistive heating is determined by the conversion of electrical energy into heat through a resistance element. Using relationships such as P = IV or P = V²/R, one can detail how voltage, current, and resistance interplay to produce the desired heating power, ensuring that the heater can deliver the calculated thermal energy consistently over time.

Ohm's Law and Circuit Analysis

Ohm's Law, which states that V = IR, is fundamental in understanding how current, voltage, and resistance relate in an electrical circuit. In the context of designing an immersion heater, Ohm's Law is used to determine the necessary current flow and to calculate the required resistance for the heating element to operate at a specified voltage while delivering the desired power output.

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