A student uses an immersion heater to heat 0.30 kg of water from 20^∘ C to 80^∘ C for tea. (a)

step 1 Let's start from the first part of this problem. In this case, we have to describe a relationshi

A student uses an immersion heater to heat 0.30 kg of water...

A student uses an immersion heater to heat $0.30 \mathrm{~kg}$ of water from $20^{\circ} \mathrm{C}$ to $80^{\circ} \mathrm{C}$ for tea. $(\mathrm{a})$ If the heater is $75 \%$ efficient and takes $2.5 \mathrm{~min}$ to heat the water. what is its resistance? (b) How much current is in the heater? (Assume 120-V household voltage.)

Key Concepts

Current Calculation in Electrical Circuits

After determining resistance, the current flowing through an electrical component can be calculated using I = V / R, where I is the current, V is the voltage, and R is the resistance. This concept is essential for assessing the electrical load and ensuring that circuits operate within safe parameters.

Heat Energy Calculation with Specific Heat Capacity

This concept involves determining the amount of thermal energy needed to increase the temperature of a substance. It uses the formula Q = m · c · ?T, where Q is the heat energy, m is the mass, c is the specific heat capacity, and ?T is the change in temperature. This calculation is fundamental in understanding how much energy must be supplied to achieve a desired temperature increase.

Efficiency in Energy Transfer

Efficiency represents the ratio of useful energy output to the total energy input, reflecting the losses (such as heat loss or other inefficiencies) in the energy conversion process. In electrical heating devices, knowing the efficiency allows us to determine the actual energy supplied to heat the medium relative to the total electrical energy consumed.

Electrical Energy and Power Relationship

This concept defines the relationship between energy, power, and time through the equation E = P · t, where E is energy, P is power, and t is time. It provides a bridge between the energy requirements calculated from thermal needs and the electrical power supplied by the heater over a specific period.

Ohm’s Law and Resistive Power Dissipation

Ohm’s Law, which relates voltage, current, and resistance (V = I · R), is crucial in analyzing electrical circuits. In resistive heating, the power dissipated can be expressed as P = V² / R or P = I² · R. This relationship allows for calculating the resistance of a heating element when the power and voltage are known.

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