Seebeck Voltage [closed]

Question

I understand that the voltage of two metal elements is V=(Sb-Sa)(T2-T1) regarding a thermocouple. But, what if mass was introduced to find the voltage? Can mass also be used to find voltage with Seebeck coefficients and temperature differences? If so, how would I incorporate mass of the thermocouple into the formula?

Answer 1

There are several ways to approach this.

1. You have given the equation in your question. It does not contain a mass term. Therefore mass plays no part.

2. Let's say you have a Seebeck junction, and you double its mass in a way that preserves its topology, ie what is connected to what. That means that you can consider the larger junction could be comprised as two of the original junctions in parallel. The voltage they develop into an open circuit will be the same.

As there are two junctions in parallel, they will be able to deliver a larger current into an external circuit than the original junction. If you want to stretch 'what a Seebeck does' into the realm of supplying a current (normally when you measure the Seebeck voltage it's into an open circuit), then a higher mass junction will deliver a higher voltage to an external circuit. However this effect is correctly handled by taking account of the resistance of the junction, rather than trying to mash the mass into the Seebeck voltage equation - the former will correctly predict what the current will be into various loads, the latter will not.

If you change the topology, say put the two junctions in series rather than parallel, then you will double the voltage. This is better handled by addressing the topology directly, not approaching it through the mass of the junctions.

3. There is a systematic way to handle questions like this, Dimensional Analysis.

The quick summary of this is that all measured quantities have dimensions, which include length, time, mass, current etc, and if you have a quantity like length for instance, you can't measure it in seconds or kg, only inches or metres.

The poster-boy for this method is perhaps the period of a pendulum, where you have to find a way to make 'seconds' from a number of things like bob mass, pendulum length, temperature, gravitational acceleration. It turns out that sqrt(length/acceleration) has units of seconds, and mass and temperature are not needed at all. That's as far as you can go with dimensions, you have to turn to physics or experiment to find the proportional constant for any given system of units.

The longer statement of this principle adds 'multiplied by any power of any dimensionless combination of units'. Such things are often called numbers (as they are dimensionless), perhaps the best known being Reynolds Number. Again you have to go to physics or experiment to find out which of these dimensionless numbers are significant in any given situation.

Given that voltage is defined in terms of the Ampere and some work units that have mass in them (it has dimensions M.L².T^-3.I^-1), it may be worth you building some dimensionless combinations that have both mass and voltage in them. Ultimately, you would need experiment to show which of these terms are needed and which not. However, just looking at the voltage dimensions, good luck with trying to cancel out that T^-3 term!

Answer 2

Mass adds a time delay to the measurement, the more mass there is the bigger the delay. You can think of mass like capacitance. The delay will also be determined by the thermal resistance of the junction. Usually you can model the effects as a first order thermal RC circuit.

Answer 3

If you increase the mass of a thermocouple by fattening up the wires you'll decrease the resistance so more current can be drawn for a given voltage drop.

You will also increase the heat loss from heat flowing down the wires. There is no free lunch.

But (with no load) the voltage does not change.

It's analogous to a battery- the voltage is set by the chemistry and state of charge of the battery. Putting many batteries in parallel does not change the voltage.

On the other hand if you can thermally parallel thermocouples but electrically connect them in series you can get more (n times) the open-circuit voltage (with n times the resistance and n times the heat flow). This principle is used in thermopiles (and in TEC thermoelectric devices).