Explore Thomson’s effect formula, its relation to Seebeck & Peltier effects, and its significance in thermoelectric devices.
Understanding the Thomson’s Effect Formula
In the realm of thermoelectricity, Thomson’s effect is a crucial concept, discovered by Sir William Thomson (later known as Lord Kelvin) in 1851. It involves the heating or cooling of a conductor when subjected to a temperature gradient and electric current simultaneously. In this article, we will explore the formula that governs this phenomenon and its significance in the field of thermodynamics.
Thomson’s Effect Formula
The Thomson’s effect formula is represented by the following equation:
Q = JQ / Je = κT
Here,
- Q is the heat absorbed or evolved per unit charge,
- JQ is the heat current,
- Je is the electric current,
- κ is the Thomson coefficient, and
- T is the absolute temperature.
Thomson Coefficient
The Thomson coefficient (κ) is a material property that determines the amount of heat absorbed or evolved due to the Thomson effect. It depends on the temperature and the nature of the conductor. A positive Thomson coefficient indicates that the conductor absorbs heat when the electric current flows from a hotter region to a cooler region. In contrast, a negative Thomson coefficient means that the conductor evolves heat under the same conditions.
Relationship with Seebeck and Peltier Effects
Thomson’s effect is closely related to two other thermoelectric effects, namely the Seebeck effect and the Peltier effect. The Seebeck effect is the generation of an electromotive force (EMF) in a conductor when it is subjected to a temperature difference, while the Peltier effect refers to the heating or cooling of a junction between two dissimilar conductors when an electric current passes through it.
These three effects are interconnected, and their relationship is established by the following equations:
- Seebeck coefficient (S) = dV / dT
- Peltier coefficient (Π) = S × T
- Thomson coefficient (κ) = dΠ / dT
These relationships show that the Thomson coefficient is the temperature derivative of the Peltier coefficient, which in turn is the product of the Seebeck coefficient and temperature.
Applications and Significance
Thomson’s effect plays a crucial role in thermoelectric devices such as thermocouples, Peltier coolers, and thermoelectric generators. Understanding the Thomson’s effect formula and its relationship with other thermoelectric effects is essential for optimizing the performance of these devices, improving energy efficiency, and developing new materials with enhanced thermoelectric properties.
Example of Thomson’s Effect Calculation
Let’s consider a hypothetical conductor with a given Thomson coefficient (κ) and temperature gradient to demonstrate how to calculate the heat absorbed or evolved due to the Thomson effect.
Assume the following values:
- κ = 0.0015 W/A·K
- T = 300 K
- Je = 2 A (electric current)
According to the Thomson’s effect formula:
Q = JQ / Je = κT
We can find the heat absorbed or evolved per unit charge (Q) by substituting the given values into the formula:
Q = (0.0015 W/A·K) × (300 K)
Q = 0.45 W/A
Now, we can calculate the heat current (JQ) by multiplying Q by the electric current (Je):
JQ = Q × Je
JQ = (0.45 W/A) × (2 A)
JQ = 0.9 W
In this example, the conductor absorbs 0.9 watts of heat due to the Thomson effect. Since the Thomson coefficient is positive, the conductor absorbs heat when the electric current flows from a hotter region to a cooler region.
