Seebeck Effect

I guess you never heard of a thermocouple, to dissimilar metals joined at a junction for the purpose a small voltage proportional (sort of) to the temperature of the junction.

Strange since you lifted this equation, , directly from the Wikipedia article on thermo-electricity. All you need is a list of the Seebeck coefficients for various combinations of conductors and you can calculate the output voltages.

>can the conducting metals can be any metals i.e., any metals that we come across everyday

The answer is yes, any two dissimilar metals qualify for the Seebeck effect. But you have to understand that the Seebeck effect is the generation of a voltage potential across a temperature gradient. The opposite edges of a clad quarter do not vary enough in temperature to create a significant voltage drop.

>what is the emf developed with certain corresponding temperature?

If you stick with the commonly available commercial thermocouples then there are published tables that define the voltage vs temperature relationship (assuming cold junction/ice point compensation). The assumption is that the thermocouple metals/alloys' composition conforms to the published standards. The acceptable uncertainty, by the way, is significant as the ANSI table below shows, ±4 Deg F for a standard limit-of-error element.

Once you invent your own thermocouple, then you bear the responsibility for generating the appropriate tables, and the appropriate specs for the materials, meaning alloy analysis that is generally defined by analytical spectroscopic methods.

If you're so inclined to dabble outside commercial thermocouple thermometry, you can pick up a copy of P.A. Kinzie's Thermocouple Temperature Measurement (John Wiley & sons, 1973). He documents hundreds of thermocouple metal combinations, both noble and base metal, that are not commonly used commercial varieties. It makes for great bed time reading.