Limit to the amountof heat contained in a rod?

[A Dhingra]

limit to the amountof heat contained in a rod??

Hi.
I just wanted to know is there any limit to the amount of heat energy that a body can store in itself? For example, we have a rod of copper and one of its end is in contact with a source of heat (at the maximum temperature of 373 K), the rod is insulated on its curved surface and open at the ends. The supply of heat continues for long time, (as in till the time we want), Should there be a point when the rod cannot take in anymore amount of heat? Well, I suppose there should be, as that would be the reason why the rod will reach an equilibrium state with temperature becoming fixed at every point along the length of the rod.
So can someone please explain how is it that the heat a body can contain in itself has to have a limit? Please provide arguments in this regard.

One more thing, are there any chances of existence of any metastable equilibrium state here, before the final equilibrium state? If yes, can you please explain how will that occur?
(note: all I know about metastable equilibrium state is that" Metastability describes the behaviour of certain physical systems that can exist in long lived states that are less stable than the system's most stable state.")

Thanks for any help in advance...

 

[AJ Bentley]

You haven't said what happens at the other open end of the rod.
Is it held at some temperature? or connected to a heat sink or is it open to radiate?

 

[A Dhingra]

I said it is open...so can radiate or there is water flow by its side taking heat away by convection. Anyhow, loss of heat from this open end is allowed.. (if it is in contact with the environment then heat loss can only occur till the temperature of the rod at this end is equal to the ambient temperature).

 

[AJ Bentley]

In that case, heat will be radiated from the end according to the 4th power of the temperature.
An equilibrium will be reached when the heat supply at the one end at 373°K matches the heat loss at the other.
It's exactly analogous to flow of electric current down a conductor of fixed resistance (conductivity) where one end is at a fixed voltage and the other subjected to a current drain given by the 4th power of the voltage at that end.

 

[A Dhingra]

well, honestly I wanted to understand how is this equilibrium state reached and the reason that appeared sensible to me was may be there is a limit to the amount of heat it can use to raise its temperature, when a maximum of temperature for given conditions is reached the heat entering just leaves... And here the argument looks like circular..
Okay, let me try this way, Some amount of heat is continuously supplied to the rod, so the rod should be able to raise its temperature with it. But the maximum temperature is supposed to be that of the source. But in practice the maximum temperature of the rod at some distance from the source is always less than that of the source.

 

[Borek]

Okay, let me try this way, Some amount of heat is continuously supplied to the rod, so the rod should be able to raise its temperature with it. But the maximum temperature is supposed to be that of the source. But in practice the maximum temperature of the rod at some distance from the source is always less than that of the source.

If the rod were perfectly insulated (good luck with it) its temperature should be identical everywhere and it should be no longer able to get any more heat. At this stage amount of heat in the rod will be constant,

In reality it will be always losing heat as there is no such thing as a perfect insulation, so there will be a temperature gradient and your source will be all the time supplying heat - but not to the rod! After getting to steady state conditions in the rod, heat will be used to heat the surroundings, and amount of heat contained within the rod will be constant (but slightly smaller than in the first case).

 

[AJ Bentley]

Not quite. (reply to OP)
The rod is not a perfect conductor so at equilibrium there is a temperature gradient along it from 373 at one end to something less at the other.

As I said, it's exactly the same as the electrical analogy. The amount of heat = the amount of electricity(charge). Temperature = Voltage. Current = Heat flow. Thermal Conductivity = Electrical Conductivity

Heat is being sucked out of the source, transported along the rod and supplied to the sink at the other. The precise value of the heat flow depends on the rate at which the sink takes it from it's end of the rod.
If it's a poor sink and doesn't take much heat, the temperature at that end rises so that overall the average temperature of the rod is higher, but it's still a gradient.
If the sink ceases to take heat at all, the temp rises to a uniform 373 along the rod.

Meanwhile, at the other end, the source supplies whatever is demanded of it to keep it's end of the rod at 373. It supplies exactly what the sink requires. (Assuming it has infinite resources to hold it's temperature.)