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why same type of cable (Copper in case of K-Type) is used as extension of Thermocouples?

in some cases same ie Alumel and Cromel is used? what could be the reason behind it?

It's to avoid creating another junction of dissimilar metals and distorting the temperature measurement you're trying to make.

Just to clarify, a Type K thermocouple does NOT use copper wire as extension cable.

Even a Type T thermocouple which is composed of copper alloys does not use ordinary copper wire as extension wire, it uses type T extension cable.

The extension cable must match the type thermocouple to get any confidence that there are not intermediate junctions.

If your application requires copper wire runs then you need to use a thermocouple temperature transmitter, widely used in process industries with long wiring runs. The connection between the receiver (DCS/PLC/controller/indicator) and the transmitter is copper wire because the output is 4-20mA, a current signal proportional to temperature.

Type K extension cables are not equivalent to Type K t/c wires, but is much cheaper. The use of the extension wire alloys is that they produce similar emf's as the base type but only at ambient temperatures.

Have seen copper extension wiring used where the end user makes the emf correction in the displayed temperature reading. Less accurate, no, but that approach is used to simplify the wiring and the need to separately pull T/C extension wires. Only used where the errors are properly assessed and dealt with.

> Just to clarify, a Type K thermocouple does NOT use copper wire as extension cable.

The whole point of using thermocouple extension wire is to bring the "cold" junction back to where it can measured so that cold junction measurement can be used for in the cold junction compensation calculation.

Yes, one can make an assumption about what a remote cold junction temperature is and calculate the compensation based on that assumption, but in a world of readily available t/c extension wire (or transmitters), why? Every degree of cold junction temperature deviation from the assumed CJ temp is an error of the same magnitude.