Kohlrausch Apparatus

Kohlrausch Apparatus

The Kohlrausch method involves the determination of the product of the thermal conductivity (λ) and the electrical resistivity (ρ). Since the electrical resistivity is also measured at the same time, conductivity can be calculated. The method involves passing constant direct current through the specimen to heat the sample while the ends are kept at constant temperature. Radial heat losses are minimized by an external heater maintained at the sample's midpoint temperature. With these provisions, at steady state a parabola-like axial temperature profile is obtained. Thermocouples are placed at the center and one centimeter on each side of the center. The thermocouples also act as voltage probes. Numbering the center thermocouple as the "2" position and the other positions as "1" and "3", it is possible to get the product of λ and ρ:

λρ=V²/(4[2T₂-(T₁+T₃)]

The top and bottom temperatures, T₁+T₃ are summed and the middle, T₂, is the middle temperature. Since the electrical resistivity can be obtained during measurements from the following equation:

ρ=(A/L)(V/I)

where V is the voltage drop between the top and bottom thermocouples, A is the cross sectional area, I is the current, and L is the distance between the top and bottom thermocouples, λ can be calculated. The data collection (T₁, T₂, T₃, V₃ - V₁, I) are computerized and the results calculated for a set of measurements performed while the sample is under vacuum and the heater temperature matched to that of T₂. For a new temperature point, additional current is used, a new set of equilibrium conditions is obtained, and the process repeated.