Thermocouple woes

Looking at the Wikipedia page on thermocouples I found this table:

Type	Temperature range °C (continuous)	Temperature range °C (short term)	Tolerance class one (°C)	Tolerance class two (°C)	IEC Color code	BS Color code	ANSI Color code
K	0 to +1100	−180 to +1300	±1.5 between −40 °C and 375 °C ±0.004×T between 375 °C and 1000 °C	±2.5 between −40 °C and 333 °C ±0.0075×T between 333 °C and 1200 °C
J	0 to +750	−180 to +800	±1.5 between −40 °C and 375 °C ±0.004×T between 375 °C and 750 °C	±2.5 between −40 °C and 333 °C ±0.0075×T between 333 °C and 750 °C
N	0 to +1100	−270 to +1300	±1.5 between −40 °C and 375 °C ±0.004×T between 375 °C and 1000 °C	±2.5 between −40 °C and 333 °C ±0.0075×T between 333 °C and 1200 °C
R	0 to +1600	−50 to +1700	±1.0 between 0 °C and 1100 °C ±[1 + 0.003×(T − 1100)] between 1100 °C and 1600 °C	±1.5 between 0 °C and 600 °C ±0.0025×T between 600 °C and 1600 °C			Not defined.
S	0 to 1600	−50 to +1750	±1.0 between 0 °C and 1100 °C ±[1 + 0.003×(T − 1100)] between 1100 °C and 1600 °C	±1.5 between 0 °C and 600 °C ±0.0025×T between 600 °C and 1600 °C			Not defined.
B	+200 to +1700	0 to +1820	Not Available	±0.0025×T between 600 °C and 1700 °C	No standard use copper wire	No standard use copper wire	Not defined.
T	−185 to +300	−250 to +400	±0.5 between −40 °C and 125 °C ±0.004×T between 125 °C and 350 °C	±1.0 between −40 °C and 133 °C ±0.0075×T between 133 °C and 350 °C
E	0 to +800	−40 to +900	±1.5 between −40 °C and 375 °C ±0.004×T between 375 °C and 800 °C	±2.5 between −40 °C and 333 °C ±0.0075×T between 333 °C and 900 °C
Chromel/AuFe	−272 to +300	n/a	Reproducibility 0.2% of the voltage; each sensor needs individual calibration.

I also had a closer look at the sheaths that the wires for the thermocouple are insulated with. The one going to the +ve port had red lines and the one to the -ve port had what appeared to be black lines in it. The background colour is white.

Based on that table then and if we assume the black is actually a very dark blue then the thermocouple used is most likely going to have been a K type which appear to be fairly popular so it should be easy to find a new one.

With 41 µV/°C I can calculate the maximum voltage I'll need to be able to spoof the thermocouple up to 600°C. I picked this as it shouldn't even go close but in case it does I can still test it.

With 3.3V avaliable from an old ATX PSU and (with some help from here) a voltage of 25.703mV(measuring 600°C reference 20°C) accross the thermocouple:

Voltage drop across fog machine=0.025703V

Voltage drop across resistors=3.274297V

Current flow from fog machine=V/R

                                                 =0.025703/1000 000

                                                 =0.000000026A

Resistance required=V/I

                               =3.274297/0.000000026

                               =125934500Ω

                               =125934.500kΩ

                               =125.934500MΩ

Which is pretty close to 126MΩ

However when I run this through KTechLab (Better than a SPICE simulator for a quick calculation) 10MΩ seems to be enough... perhaps I neglected to calculate current flow through the resistance array? I'll re-post once I have more info...

More progress on the fog machine

To test my hypothesis about the temperature sensor being a thermocouple I realized that a thermocouple would have something like an op-amp as a buffer amp and to get the low voltage up to a logic level. An op-amp has an (ideally) infinite (actually) really high input impedance. This high impedance means that the amp does not load down the input circuit with high current draw.

I=V/R
I=V/infinity
I=0

This is why an op-amp has a high input impedance.

The temperature probe connections have a resistance of around 1000k. That's pretty high, which when coupled with the polarity markings indicates that there is an op-amp on the board and the temperature probe is a low current voltage source. Also known as a thermocouple.

This means I can now simulate the presence of the temperature probe by supplying an appropriate voltage(not sure how big yet though). By simulating the presence of the thermocouple I can test if the electronics will turn off the heater current at some point which means that it was just the thermocouple that failed. The outer braid of the thermocouple has failed where it enters the remains of the aluminium so that makes me think that something went badly wrong with the thermocouple.

While I had the multimeter out I also measured the heater coil's resistance- this came out at about 700k. So with a little math we can calculate the current flowing through the coil and also the wattage(not really that important but might be interesting to see how much power the electronics use).

I=V/R
I=230/700k  (Pretty sure 230V isn't RMS but I know it isn't Peak to Peak so it shouldn't give us a number that is too high)
I=230/700 000 (Now in SI units)
I=0.003288571A    (Seems very very low ???)

Now for power consumption:

P=IV
P=230*0.003288571
P=0.76W

This is clearly wrong so I decided to check again... It turns out that my fingers have a resistance of around 700k ohms and it was this resistance I measured. The heating coil appears as an open circuit so I think I'm going to have to melt out the remains of the Aluminium block and get a closer look.