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Electric heating of water

An electric heater (an immersion heater) is placed in a given quantity of water at a prescribed temperature (say, 23°C). The heater is turned on, voltage and charge current for the heater and the temperature of the water are measured as functions of time. Typically, voltage and electric current can be kept constant. It is observed that the temperature of the water rises steadily (Figure 1). When the process is repeated with the same quantity of water at the same initial temperature, but with different values of voltage and electric current, the temperature of the water rises linearly again, this time at a different rate. Measurements show that the rate at which the temperature rises is proportional to the product of voltage and electric current.

Interpretation

The phenomenon demonstrates the coupling of two processes: The electric process drives a thermal one, i.e., the heating of the water. Since we have the same amount of water starting under equal conditions every time, we can interpret the different rates at which the temperature rises as the result of different “efforts” of the electric process. If the temperature rises slowly, electricity is not “working so hard,” whereas if it rises quickly, the electric system is “working hard.” It is customary to introduce the notion of power to describe how “hard” a system is “working.” Expressed differently, the power of the electric process measures at what rate the electric system is driving the thermal process.

The experiment shows that the power of the electric heater is higher the faster the temperature of the water is rising. Data shows that the temperature rises more quickly if voltage and electric current are higher. The product of voltage and current of charge is proportional to the slope of the temperature curves in Figure 1. Power is understood as the rate at which the driving process releases energy or, vice-versa, the rate at which the driven process uses energy (Figure 2, and the chapter on Energy).