Answer the question about time of cooling of a ball

[Hurcane]

Homework Statement

Answer the following question:
"In which of the cases will the cooling time be the least:
1. the ball is suspended from the ceiling
2.the ball lies on a stand with a thermal conductivity greater than the thermal conductivity of the ball
3. is the ball lying on a stand with a thermal conductivity lower than the thermal conductivity of the ball?"

Relevant Equations

-

Hello, I'm not sure if this is the right place to post my question, however I still want to know. Recently, my teacher asked me the following question:
"In which of the cases will the cooling time be the least:
1. the ball is suspended from the ceiling
2.the ball lies on a stand with a thermal conductivity greater than the thermal conductivity of the ball
3. the ball lying on a stand with a thermal conductivity lower than the thermal conductivity of the ball"
I am not strong in physics, so I could not fully state the answer.
Thank you in advance for any help.

 

[berkeman]

Welcome to PF.

What do you think is the correct answer and why? And why is #3 a question instead of statements like #1-#2?

 

[Hurcane]

Hi!

Number three should be the statement, this is my mistake. As for my opinion on the question, I believe that the ball will cool down the longest in case #1, and the least in case #2, case #3 will be between case #1 and case #2. But I can't back it up with any formulas.

Welcome to PF.

What do you think is the correct answer and why? And why is #3 a question instead of statements like #1-#2?

 

[berkeman]

I think that is close to correct. Does the problem mention what temperatures the ball, air and stand are at initially?

 

[Hurcane]

I think that is close to correct. Does the problem mention what temperatures the ball, air and stand are at initially?

No, but as far as I understand, it is assumed here that the temperature of the ball is higher than the temperature of the stand, and the air temperature is much lower than the temperature of the ball. The temperature of the stand is most likely the same as the air temperature (according to Newton's cooling law).

 

[kuruman]

Question for @Hurcane: Which pair of conductivities makes more sense to compare in order to answer 3? Remember that something with very low thermal conductivity is called a thermal insulator.

A. Air and ball
B. Air and stand
C. Ball and stand

 

[Hurcane]

Question for @Hurcane: Which pair of conductivities makes more sense to compare in order to answer 3? Remember that something with very low thermal conductivity is called a thermal insulator.

A. Air and ball
B. Air and stand
C. Ball and stand

As far as I know, air is a strong thermal insulator. Therefore, the ball in case #1 will cool down more slowly than in case #3, right?

 

[kuruman]

As far as I know, air is a strong thermal insulator. Therefore, the ball in case #1 will cool down more slowly than in case #3, right?

We are told that the conductivity of the stand is lower than that of the ball. What if it’s also lower than that of the air?

 

[Hurcane]

We are told that the conductivity of the stand is lower than that of the ball. What if it’s also lower than that of the air?

I don't think this condition is implied in the task. But if we consider it, it turns out that the longest cooling time will be in case #3

 

[kuruman]

I don't think this condition is implied in the task. But if we consider it, it turns out that the longest cooling time will be in case #3

I agree.

 

[PeroK]

I don't see that the question is complete. Case #3 could be an insulating stand with better insulation that air. It simply doesn't say.

 

[Steve4Physics]

I don't see that the question is complete. Case #3 could be an insulating stand with better insulation that air. It simply doesn't say.

Maybe it's even more complicated...

Cooling of the ball will be due a mixture of conduction, convection and radiation. If the ball has only a tiny contact-area with the (say flat) stand, then conduction from the ball to the stand might be negligible! And the presence of the stand might reduce convective losses!

 

[Lnewqban]

Copied from
https://en.m.wikipedia.org/wiki/Thermal_conduction#Fourier's_law

“The law of heat conduction, also known as Fourier's law, states that the rate of heat transfer through a material is proportional to the negative gradient in the temperature and to the area, at right angles to that gradient, through which the heat flows.”

Welcome, Hurcane!