What happens to the temperature of the container during phase change of the substance contained inside

Question

I know that as the phase of a substance changes the temperature of the substance remains constant. Now, I was wondering what would happen to the temperature of the container (assuming during the phase change of the substance contained in the container, the container itself doesn't undergo phase change) when the substance contained in the container was undergoing phase change.

I searched the web for any clue but could not find anything regarding the temperature of the container.

Would the temperature of the container go up or remain constant if heat is being supplied at a constant rate to the system(system containing the container and the substance undergoing phase change).

I think the temperature of the container depends upon the conductivity of the substance undergoing phase change. If the conductivity of the substance undergoing phase change is more than the container then the temperature of the container would remain same and if the conductivity of the substance is less than that of the container then the temperature of the container rises.

I am not sure if my line of reasoning is correct, hence would like to have some conformation regarding the same and do support your statement by a sound reasoning.

Answer 1

For heat to be transported by conduction through the container there must be a temperature gradient, so if heat is coming into the container then the outside of the container must be at a higher temperature than the inside of the container.

Answer 2

Elementary thermodynamics tells us that during phase change a system can absorb or release heat without changing its temperature. You have to give to (or take from) the system a certain quantity of energy to have it complete phase transition: this energy must come from (or go to) somewhere.

Think about a block of ice at temperature 0 Celsius, immersed in water. To melt this quantity of ice, water must give heat to the block until fusion is complete. In this heat exchange, water's temperature decreases.

That's the same case as yours, when you consider the water as the container. If you provide heat to the system, the situation can change wildly, but the basic rule is to use the first principle and think in terms of energy exchanges.

Answer 3

If the substance is entirely enclosed by the container, the container has the job to transport the heat to or away from the substance in order to keep the phase change going.

In case heat has to be supplied to the substance for the phase change, then the container will always be at a higher temperature than the substance itself, because heat always flows from hot to cold temperature. If the container would have the same temperature, then the heat flux to the substance would come to a halt.

There will also be a temperature gradient along the container wall, so the outer side of the container is hotter than the inner side.

The actual temperature difference between the container and the substance depends on many factors like total heat rate, thermal conductivity, motion of the substance etc.