An immersion-type heating coil is connected to a 120 -V outlet and immersed in a \(250-\mathrm{mL}\) cup of water initially at \(10^{\circ} \mathrm{C}\). The water comes to a boil in 85 s. Assuming no heat loss, and neglecting the heater's mass, find (a) the power and (b) the heater's resistance.

Understanding how thermal energy moves from one object to another is crucial when evaluating how a heating element like an immersion heater works. Thermal energy transfer refers to the movement of heat from a warmer area to a cooler one.

The process of heating water in the described exercise involves the transfer of thermal energy from the heating coil to the water. This occurs through conduction, as the electrically heated coil comes into direct contact with the water, causing water molecules to increase their kinetic energy, leading to an increase in temperature until it reaches the boiling point.

There are no heat losses considered in this scenario, which simplifies calculations but is an idealization. In real-world scenarios, some heat would be lost to the surroundings.

A fundamental concept in electrical circuits is Ohm's Law, which relates the current flowing through a conductor to voltage and resistance. It is usually expressed as the equation \( V = IR \), where \( V \) is the voltage across the conductor, \( I \) is the current flowing through it, and \( R \) is the resistance.

In the context of the immersion heater exercise, Ohm's Law helps us find the resistance of the heater. Given a constant voltage supplied by the outlet and the power consumed by the heater, we can manipulate Ohm's Law to calculate resistance. Ohm’s Law is foundational for understanding how electrical devices like heaters function when connected to a power source.

The specific heat capacity is a property of a material that measures the amount of heat needed to raise the temperature of one kilogram of the material by one degree Celsius (or one Kelvin). In the formula \( Q = mc\Delta T \), \( c \) represents the specific heat capacity.

In the exercise, the water's specific heat capacity is used to determine the energy required to raise its temperature from 10 to 100 degrees Celsius. The high specific heat capacity of water explains why it takes a relatively large amount of energy to change its temperature, a phenomenon that's critical in a wide range of practical applications, including the heating process of the exercise.

Electric power, measured in watts, is the rate at which electrical energy is converted into another form of energy, such as heat, light, or motion. The formula to calculate power is \( P = VI \) or, as used in our exercise, \( P = Q / t \), where \( P \) stands for power, \( Q \) for thermal energy, and \( t \) for time.

When calculating the power of the heater, we determine how much energy the heater can transfer to the water in a specific amount of time. The exercise requires students to find out how much energy is transferred in 85 seconds, highlighting the relationship between power, energy, and time. Understanding power is essential for designing and operating electrical devices efficiently and safely.