Unit 15: Thermoelectric Effects
Introduction to Thermoelectric Effects
Thermoelectric effects describe the direct interconversion between temperature differences and electric voltage in certain materials. When a temperature gradient exists across a conductor or semiconductor, charge carriers diffuse from the hot to the cold end, generating an electromotive force (EMF). Conversely, passing an electric current through a junction of two dissimilar materials can cause heat to be absorbed or released. These reversible phenomena are known as the Seebeck effect and the Peltier effect, respectively. Together with the Thomson effect, they form the foundation of thermoelectric technology used in sensors, generators, and coolers.
1. Seebeck Effect and Thermocouples
Definition and Physical Basis
The Seebeck effect, discovered by Thomas Johann Seebeck in 1821, states that a voltage (EMF) is generated when two dissimilar electrical conductors or semiconductors form a closed loop and their junctions are maintained at different temperatures. The generated EMF depends solely on the materials involved and the temperature difference between the junctions.
Seebeck EMF: 𝒞 = ∫_{T₁}^{T₂} (S_A(T) - S_B(T)) dT
where S_A(T) and S_B(T) are the temperature‑dependent Seebeck coefficients (in V/K) of materials A and B, and T₁ and T₂ are the temperatures of the two junctions.
For small temperature ranges where the Seebeck coefficients can be considered constant, the expression simplifies to:
𝒞 ≈ (S_A - S_B) (T₂ - T₁) = 𝒮 ΔT
Here, 𝒮 = S_A - S_B is the relative Seebeck coefficient of the pair, and ΔT = T₂ - T₁ is the temperature difference.
Thermocouple Construction
A thermocouple consists of two wires of different metals (or alloys) joined at two points, forming two junctions:
- Measurement (hot) junction – placed at the point whose temperature is to be measured.
- Reference (cold) junction – kept at a known, stable temperature (often 0 °C using an ice bath or electronically compensated).
The EMF generated between the open ends of the wires is measured with a voltmeter. Because the EMF is a function of both the temperature difference and the material pair, thermocouples serve as robust, wide‑range temperature sensors.
Laws Governing Thermocouple EMF
- Law of Homogeneous Circuits: A temperature‑gradient‑induced EMF cannot be produced in a single homogeneous conductor; a circuit must contain at least two different materials.
- Law of Intermediate Metals: Inserting a third metal into a thermocouple circuit does not alter the net EMF, provided the two new junctions are at the same temperature.
- Law of Successive or Intermediate Temperatures: The EMF produced by a thermocouple between temperatures
T₁andT₃equals the sum of the EMFs forT₁→T₂andT₂→T₃whenT₂is an intermediate temperature.
Seebeck Coefficients and Material Selection
The magnitude of the Seebeck coefficient varies widely among materials. Common thermocouple types are standardized by the International Electrotechnical Commission (IEC) and are chosen based on temperature range, sensitivity, stability, and environmental resistance.
| Thermocouple Type | Positive Leg | Negative Leg | Typical Temperature Range (°C) | Approx. Seebeck Coefficient (µV/°C) |
|---|---|---|---|---|
| K (Chromel‑Alumel) | Ni‑Cr (Chromel) | Ni‑Al (Alumel) | -200 to +1250 | ≈ 41 |
| J (Iron‑Constantan) | Fe | Cu‑Ni (Constantan) | -210 to +1200 | ≈ 55 |
| T (Copper‑Constantan) | Cu | Cu‑Ni (Constantan) | -200 to +350 | ≈ 43 |
| E (Chromel‑Constantan) | Ni‑Cr (Chromel) | Cu‑Ni (Constantan) | -200 to +900 | ≈ 68 |
| N (Nicrosil‑Nisil) | Ni‑Cr‑Si (Nicrosil) | Ni‑Si‑Mg (Nisil) | -200 to +1300 | ≈ 39 |
| S (Platinum‑Rhodium 10%/Pt) | Pt‑10%Rh | Pt | -50 to +1750 | ≈ 10 |
| R (Platinum‑Rhodium 13%/Pt) | Pt‑13%Rh | Pt | -50 to +1750 | ≈ 12 |
| B (Platinum‑Rhodium 30%/6%) | Pt‑30%Rh | Pt‑6%Rh | 0 to +1800 | ≈ 0 (very low sensitivity below 300 °C) |
Applications of Thermocouples
- Industrial temperature measurement: Furnaces, kilns, gas turbines, and exhaust systems.
- Scientific research: Cryogenics, high‑temperature physics, and materials testing.
- Home appliances: Ovens, water heaters, and HVAC systems.
- Automotive: Engine exhaust gas temperature (EGT) sensors.
2. Peltier Effect and Thermopile
Definition and Physical Basis
The Peltier effect, discovered by Jean Charles Athanase Peltier in 1834, is the converse of the Seebeck effect: when an electric current passes through a junction of two dissimilar conductors, heat is either absorbed at one junction and liberated at the other, depending on the direction of current flow. The heat absorbed or released per unit time (Peltier heat) is proportional to the current.
Peltier heat rate: Q_Π = Π I = (S_A - S_B) T I
where Π is the Peltier coefficient (in V), I is the electric current (A), T is the absolute temperature of the junction (K), and S_A - S_B is the relative Seebeck coefficient.
The sign of Q_Π indicates heat absorption (Q_Π > 0) or release (Q_Π < 0) at the junction where current flows from material A to B.
Variation of Thermo‑electric EMF with Temperature
Both Seebeck and Peltier coefficients are temperature dependent. For many metals and alloys, the Seebeck coefficient varies approximately linearly with temperature over moderate ranges:
S(T) = S₀ + α T
where S₀ is the Seebeck coefficient at 0 K and α is the temperature coefficient (µV/K²). Consequently, the EMF generated by a thermocouple is not perfectly linear; calibration curves or polynomial fits are used for precise temperature measurement.
Thermopile: Series Connection of Thermocouples
A thermopile consists of multiple thermocouple pairs connected electrically in series and thermally in parallel. By summing the EMFs of many junctions, a thermopile produces a significantly larger voltage for a given temperature difference, thereby increasing sensitivity and enabling detection of weak thermal radiation.
The total EMF of a thermopile with N identical couples is:
𝒞_total = N × 𝒮 ΔT
where 𝒮 is the relative Seebeck coefficient of each couple and ΔT is the temperature difference between the hot and cold sides of the pile.
Applications of Thermopiles
- Infrared (IR) detection: Thermopiles are the sensing element in non‑contact IR thermometers, flame detectors, and gas analyzers. They absorb IR radiation, raising the temperature of the hot junctions relative to the cold junctions, which generates a measurable voltage.
- Power generation (Seebeck generators): When a temperature gradient is maintained across a thermopile (e.g., using waste heat or solar concentrators), the generated EMF can drive a load, providing solid‑state power without moving parts.
- Thermal flow sensors: By measuring the voltage difference caused by convective cooling of one side of the pile, fluid flow rates can be inferred.
- Temperature gradient sensors: Used in geophysical probes to measure subsurface thermal gradients.
Practical Examples and Calculations
Example 1: Thermocouple Voltage Calculation
A Type K thermocouple (Chromel‑Alumel) has its measurement junction at 350 °C and its reference junction maintained at 0 °C. Using the approximate Seebeck coefficient of 41 µV/°C for Type K:
ΔT = 350 °C - 0 °C = 350 °C𝒞 ≈ 41 µV/°C × 350 °C = 14 350 µV = 14.35 mV
The voltmeter would read about 14.35 mV, which can be converted to temperature using standard lookup tables or polynomial equations.
Example 2: Peltier Cooling Power
A Peltier module consists of many couples of Bismuth Telluride (Bi₂Te₃) with an average relative Seebeck coefficient of 200 µV/K. If a current of 2 A flows through the module at a junction temperature of 300 K:
Π = 𝒮 T = (200×10⁻⁶ V/K) × 300 K = 0.060 VQ_Π = Π I = 0.060 V × 2 A = 0.12 W = 120 mW
Thus, 120 mW of heat is absorbed at the cold junction (assuming ideal conditions). Real modules achieve a fraction of this due to Joule heating and thermal conduction losses.
Example 3: Thermopile Output for IR Detection
Consider a thermopile with 50 identical couples, each having 𝒮 = 40 µV/K. The hot junctions absorb IR radiation raising their temperature by 5 K above the cold junctions:
𝒞_total = N × 𝒮 ΔT = 50 × 40 µV/K × 5 K = 50 × 200 µV = 10 000 µV = 10 mV
A 10 mV signal is readily amplified and processed to yield temperature or intensity readings.
Summary
The Seebeck and Peltier effects are two sides of the same thermoelectric coin, enabling direct conversion between thermal gradients and electrical voltage. Thermocouples exploit the Seebeck effect for robust temperature sensing across a vast range, while thermopiles amplify this effect for sensitive detection of infrared radiation and low‑level heat fluxes. The Peltier effect provides solid‑state cooling or heating when current is driven through junctions, finding use in portable coolers, laser diode temperature stabilization, and waste‑heat recovery systems. Understanding the material‑dependent Seebeck coefficients, temperature dependence, and proper circuit laws is essential for designing accurate and efficient thermoelectric devices.