Study of the fast transient behaviour of peltier junctions

A method has been developed for measuring the temperature of a thermojunction after the passage of fast transient current pulses (30 msec to several seconds duration).

Using the model of a thermocouple whose branches are of infinite extent, it is shown theoretically that for rectangular current pulses the temperature of the cold junction is a function only of a parameter meter ζ = I√τ (I = pulse current, τ = pulse duration). The lowest temperature occurs for one particular value ζ_min of this parameter, and this temperature cannot be reduced further by any particular choice of the individual values of I and τ. In connexion with these rectangular pulses, various forms of the temperature dependence of the Seebeck coefficient are examined. For the case of logarithmic dependence, a method is developed which makes possible the determination of the temperature distribution along the couple from a measurement of the Seebeck potential as a function of time and allows the influence of the Thomson effect to be estimated.

It is further shown that, when a second rectangular current pulse is superimposed on to the first current pulse, the temperature drop due to the combined pulses may be at most twice that caused by a single pulse.

Finally it is proved, with the aid of a variational method, that the lowest transient temperature drops of the junction may be obtained with pulses for which the current is a continuous function of the time, of the form

where Θ is the time and t the time of observation.

If the pulse terminates at time t₁ and if t → t₁ then Z(Θ)_ex → ∞. Provided the current were allowed to rise indefinitely, the transient temperature would approach absolute zero if the process were not counteracted by changes in the Seebeck coefficient and the electrical and thermal conductivity which all have been assumed to be constant in this calculation.

The above results are also true for “real” thermocouples provided the length of the branches is where κ is the (average) diffusivity of the thermoelectric substances.

These calculations were essentially confirmed by experiments. With the rising current pulses, the accuracy of measurement is limited by the time resolution of the measuring circuit and by the fact that the temperature dependence of the Seebeck coefficient in this region is not known accurately. However, it is almost certain that we have observed transient temperatures well below 100°K.