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Bought from here

I have tried the magnet trick and it does not stick to either of the two wires of this TC. More so, screwing it inside an oven and turning the temperature up does produce some micro and then mili Volt reading on a DMM. However after turning the oven off the output voltage still rises for 1-2 minutes before it starts dropping.

Is this really a K-type thermocouple and if it is, is it a broken unit ?

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I have bought another such K type TC. This one responds well to the magnet on one of its wires. There was a problem with the PCB, not the TC. Fixed it and the non-magnetic TC started working as well. It seems not all K type thermocouples will have their negative wire magnetized enough for a HDD magnet to pick it.

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If a good magnet sticks to neither of the two leads it's not a K thermocouple, period, and probably not a thermocouple at all. For base-metal thermocouples (of which K is one) the negative lead is ferromagnetic.

However, I suspect you're measuring the lug, which is probably not made of thermocouple material, but rather brass or something like that. That's fine, so long as the lugs and leads are kept isothermal with extension wires or cold junction sensor.

A thermal sensor like that (in air) acts as a low pass filter with a rather long time constant (minutes) so you would expect the kind of response you are seeing. If you want fast response you need to remove the outer metal tube and expose the junction to the air, preferably with some kind of thermal transfer fin (that may not be possible with a grounded junction T/C because the wires are welded into the tip for good response in a metal block). Ribbon thermocouples can be used to measure air temperature and are reasonably fast. The time constant can cause your actual air temperature to overshoot well above the controller setpoint if you are using it as part of a control loop. This is true of any thermal sensor.

This construction of sensor would typically either be embedded in a metal block (such as a plastics mold) or immersed in a liquid.

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Thermal lag of the heat stored in the oven's steel thermal mass taking time to transfer to the air of the steel in the oven. That's normal and expected. Your PC does that too. Even if you're in direct contact with the oven, heat takes time to flow from the hottest steel parts to the cooler steel parts. If your thermocouple is not fully embedded into the steel, then the surrounding air also has a cooling effect so long as it is cooler than the surrounding steel (i.e. until it reaches the same temperature of the steel).

That's why some devices demand you not just cut power to them. You have to turn off the heat and leave the cooling (usually a fan) running for some time before turning it off or else you destroy it from overheating.

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