[jahseh]

Let's say you have a pot of water at room temperature with a thermocouple resting at the bottom of the pan. If you turn the stove on what does the plot of this curve look like?

Now I'm not sure if there is anything "special" occurring at the bottom surface of the pan where the thermal couple is laying (the bottom of the pan will be hotter than 100 C, right? maybe can assume it's not in direct contact) , but would it be a linear trend, flat line at 100 C, and increase in the vapor phase? Or would this 100C + temperature in the vapor phase not be picked up by the thermal-couple and max out at 100C?

Also, what equations can I use to aid in describing the shape of the curve? enthalpy? internal energy?

[Corribus]

Generally, you'd use the heat equation.

[Orcio_87]

(the bottom of the pan will be hotter than 100 C, right? maybe can assume it's not in direct contact)

How is this possible ? I heard that a boiling is a process for a liquid as a whole.

[jahseh]

(the bottom of the pan will be hotter than 100 C, right? maybe can assume it's not in direct contact)

How is this possible ? I heard that a boiling is a process for a liquid as a whole.

Well I figure the actual pan will get hotter than 100 C so if the thermal couple is in direct contact with the bottom then it could read higher. It's an open ended question so I'm just thinking of all the possibilities

[Orcio_87]

Walls of the pan maybe can be slightly hotter than 100 C (not too above), but liquid water will never be hotter than 100 C under normal conditions.

Also - pan = pot, or the pan is the base for the pot ?

I think it will be linear trend - from 20 to about 100 C, and then above when the water will eventually evaporate.

(about 100 C depending on pan = pot, or pan = base for the pot)

[Corribus]

The pan itself is heated by conductive heat transfer and the temperature profile in the pan would be determined using the heat equation balanced by the rate of heat input on one side (from the heat source) and the heat output on the other (from the pan to the water). The water would be primarily heated by convection, influenced by the heat source at the bottom (the pan) against evaporation at the top of the water into air. The temperature profile in space and time would depend a lot on the geometry of the pot (which would influence evaporation rate, convection currents, and radiative cooling I guess), the heat input rate, and other things like atmospheric pressure.  The pot material can exceed 100 °C. Nothing requires the temperature at the interface between two materials to be identical on both sides of the interface. In fact this is only strictly the case if there is perfect contact between the two surfaces. In reality, surfaces are not perfectly smooth and microscopic air/gas layers create a resistance to the heat transfer.

Also if your thermometer is touching the bottom of the pan, the temperature reading will be affected by the conductive heat transfer from the pan directly into the thermometer rather than from the water. This is why when you are using a thermometer in cooking, you should always have the thermometer above the surface of the pan. This is pretty much told you in any cooking show on television