Question

An iron and a constantan wire are formed into a closed circuit by connecting the ends. Now both junctions are heated and are maintained at the same temperature. Do you expect any electric current to flow through this circuit?

Short answer

Answer: No, based on the Seebeck effect, if both junctions are maintained at the same temperature, there will be no electric current flowing through the circuit.

Step-by-step solution

Understanding the Seebeck effect

The Seebeck effect is a phenomenon in which a voltage is induced in a circuit composed of two dissimilar metals when their junctions are at different temperatures. This voltage is generated due to the difference in thermoelectric properties of the metals, causing electrons to flow from the hotter junction to the cooler junction.

Analyzing the given circuit

In this exercise, we have a closed circuit with an iron and a constantan wire. The ends of these wires are connected, creating two junctions. Heating both junctions and maintaining them at the same temperature means that there is no temperature difference between the junctions.

Determine if a current will flow

Since both junctions are maintained at the same temperature in the circuit, there is no temperature difference between the junctions. Therefore, according to the Seebeck effect, no voltage will be induced in the circuit. As a result, there will be no electric current flowing through the circuit.

Conclusion

Based on the Seebeck effect, when both junctions of the circuit formed by an iron and a constantan wire are heated and maintained at the same temperature, there will be no electric current flowing through the circuit.

Key concepts

Thermoelectric Properties

When two different conductive materials are together in a circuit, their unique thermoelectric properties come into play. These properties are essentially the materials' capability to convert temperature differences directly into voltage. Different materials respond differently to heat: some produce more voltage than others when exposed to the same temperature change. This is quantified by what we call the Seebeck coefficient, which is unique to each material.

In our exercise, iron and constantan are chosen for their distinct thermoelectric properties. If these two metals were at different temperatures at their junctions, their differing Seebeck coefficients would cause a flow of electrons from the hot junction to the cooler one, producing an electric current. However, the key point is realizing the effect of maintaining the same temperature at both junctions, which exempts this scenario from generating a voltage difference due to the balance achieved between the materials.

Electric Current in Thermocouples

A thermocouple is a device that's created when two dissimilar metals, like iron and constantan in our example, form a circuit. This device is widely used to measure and control temperature because of its ability to generate a voltage signal that's dependent on the temperature difference between two points.

In the presence of a temperature gradient, an electric current flows in the loop. This current is the result of the thermoelectric potential, often referred to as the Seebeck voltage, induced across the temperature difference. More scientifically, when heat is applied, electrons within the hotter metal gain energy and diffuse towards the colder metal, causing a charge imbalance and hence a flow of current. The circuit in our example, though, doesn't exhibit a current because it's akin to a thermocouple with both junctions at the same temperature—no gradient, no current.

Temperature Difference Impact on Voltage

The relationship between temperature difference and induced voltage in a circuit containing two different metals, such as in a thermocouple, is foundational to the Seebeck effect. The greater the temperature difference between the two junctions of the metals, the higher the induced voltage will be. This is because the electron mobility in the materials is affected by temperature — at higher temperatures, electrons are more energetic and hence move more freely.

The induced voltage is therefore a form of electrical signal that's proportional to the temperature difference. To contextualize with our exercise, if the iron and constantan junctions were at different temperatures, a voltage would be induced, and its magnitude would tell us about the temperature gradient present. When the temperatures are the same, this proportional voltage is zero, illustrating that the impact of temperature difference on voltage is direct and quintessential to the behavior of thermocouples.