An electrical heating coil is immersed in 4.6 kg of water at 22^∘ C. The coil, which has a resis

step 1 In this problem, we have a heating foil that has a resistance of 250 oms, and it's put inside of

An electrical heating coil is immersed in 4.6 kg of water at...

An electrical heating coil is immersed in $4.6 \mathrm{kg}$ of water at $22^{\circ} \mathrm{C}$. The coil, which has a resistance of $250 \mathrm{f}$, warms the water to $32^{\circ} \mathrm{C}$ in $15 \mathrm{min}$. What is the potential difference at which the coil operates?

Key Concepts

Specific Heat Capacity

This concept refers to the amount of heat required to raise the temperature of a unit mass of a substance by one degree Celsius. In the context of the problem, it helps in calculating the total amount of heat energy needed to achieve the desired temperature change in the water, which is key since water’s specific heat capacity is a known constant that is widely used in thermal energy calculations.

Heat Energy Transfer

This concept involves the understanding of how energy is transferred to a substance in the form of heat. It is quantified by the product of the mass of the substance, its specific heat capacity, and its change in temperature. This calculation is essential for determining the energy absorbed by the water which is then linked to the electrical energy dissipated by the heating coil.

Electrical Power Dissipation in Resistive Heating

Resistive heating refers to the process by which electrical energy is converted into heat energy in a resistive element, such as a heating coil. This concept is crucial in the problem because the amount of electrical power dissipated in the resistor (which is related to the current, voltage, and resistance of the coil) directly correlates to the heat produced to warm the water.

Energy-Power-Time Relationship

This concept describes how energy is related to power and time, where power is defined as the rate at which energy is transferred. In thermal and electrical systems, calculating the energy (or work done) over a period requires understanding that energy equals power multiplied by the time over which the power is applied. This relationship is key to connecting the calculated heat energy with the power output of the coil over a specific period.

Voltage-Resistance-Power Relationship

This concept emerges from Ohm's law and the formula for power in electrical circuits. It explains how the potential difference (voltage) across a resistor relates to the resistance and the power dissipated by the resistor, typically expressed as power equals the square of the voltage divided by resistance. This relationship is fundamental in determining the operating voltage of the heating coil once the necessary power to achieve the heat energy requirement is known.

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