5.2 Kelvin relations in thermoelectrics

The Kelvin relations in thermoelectrics connect the Seebeck, Peltier, and Thomson effects. These fundamental equations, derived from thermodynamic principles, allow us to calculate one coefficient from another, simplifying experimental work and predicting device performance.

Understanding these relationships is crucial for optimizing thermoelectric materials and devices. The Kelvin relations highlight the importance of absolute temperature in thermoelectric phenomena and provide insights into the temperature-dependent behavior of high-performance materials.

Thermodynamic Principles

Fundamental Concepts of Thermodynamics

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• Thermodynamic reversibility describes processes that can be reversed without energy loss
• Reversible processes maintain system and surroundings in equilibrium throughout
• Ideal reversible processes form the basis for maximum theoretical efficiency calculations
• Onsager reciprocity relates flows and forces in irreversible thermodynamic processes
• Reciprocal relations connect different transport phenomena (heat flow, electrical current)
• Thermodynamic equilibrium represents a state of balance in all intensive properties
• System in equilibrium experiences no net changes in macroscopic variables over time
• Absolute temperature measures thermal energy on a scale starting at absolute zero
• Kelvin scale defines absolute zero as 0 K, equivalent to -273.15°C

Applications in Thermoelectric Systems

• Reversibility concepts help evaluate real thermoelectric device efficiencies
• Comparison to ideal reversible processes quantifies irreversible losses
• Onsager relations apply to coupled heat and charge transport in thermoelectrics
• Equilibrium conditions determine maximum voltage output in thermoelectric generators
• Absolute temperature crucial for calculating thermoelectric coefficients and efficiencies

Thermoelectric Coefficients

Seebeck Effect and Coefficient

• Seebeck effect generates voltage in a circuit with temperature difference between junctions
• Seebeck coefficient (S) quantifies voltage produced per unit temperature difference
• Measured in units of V/K or more commonly μV/K due to typical magnitudes
• Depends on material properties and temperature
• Sign of S indicates majority charge carrier type (positive for holes, negative for electrons)

Peltier and Thomson Effects

• Peltier effect describes heat absorption or release at junction of dissimilar materials
• Peltier coefficient (Π) quantifies heat transferred per unit current
• Measured in units of V or W/A
• Thomson effect relates to heat absorption or release in a single conductor with current flow and temperature gradient
• Thomson coefficient (τ) quantifies heat absorbed or released per unit current per unit temperature difference
• Measured in units of V/K

Kelvin Relations

Fundamental Kelvin Relations

• Kelvin relations connect Seebeck, Peltier, and Thomson coefficients
• First Kelvin relation links Peltier and Seebeck coefficients: $Π = ST$
• T represents absolute temperature
• Second Kelvin relation connects Thomson and Seebeck coefficients: $τ = T(dS/dT)$
• These relations derive from thermodynamic principles and Onsager reciprocity

Applications and Implications

• Kelvin relations allow calculation of one coefficient from knowledge of others
• Simplify experimental measurements by reducing number of required experiments
• Enable prediction of device performance across temperature ranges
• Provide consistency check for experimental data
• Highlight importance of absolute temperature in thermoelectric phenomena

Temperature Dependence and Material Characteristics

• Seebeck coefficient often varies with temperature, affecting other coefficients
• Temperature dependence of S leads to non-zero Thomson coefficient in many materials
• Materials with constant S over temperature range have zero Thomson coefficient
• High-performance thermoelectric materials often exhibit complex temperature-dependent behavior
• Understanding temperature dependence crucial for optimizing device performance across operating range