Differences between heat capacity and thermal conductivity/convection

[sgstudent]

Homework Statement

I learned that the heat capacity is the amount of energy absorbed to raise the temperature of a body by 1 degrees. While conduction is the process of heat transfer by vibrations. That being said, when I supply 1000N of heat to 2 rods of different material but same mass the overall temperature of the two rods will be different because of heat capacity. So where does conduction come into play here? Conduction helps to transfer the heat so is it safe to say the final temperature is the 'net' effect after there is no more conduction?

So is it possible to have an object with a low heat capacity like alcohol but with an extremely high thermal conductivity such that even when heat is supplied the other end feels cold because it has not reached the 'net' stage. And only after the heat is transferred to the other end then it will feel hot?

Lastly, for fluids will it be the same for convection?

Homework Equations

Q=CΔθ

The Attempt at a Solution

i'm thinking that they related because the heat capacity determines the temperature at that final end product while the thermal conductivity allows the heat to be transferred. So the conductive process is just the 'stabilizer'?

Thanks for the help!

 

[haruspex]

1000N of heat

What unit of heat is 'N'?

So is it possible to have an object with a low heat capacity like alcohol but with an extremely high thermal conductivity such that even when heat is supplied the other end feels cold because it has not reached the 'net' stage. And only after the heat is transferred to the other end then it will feel hot?

Yes. That's the main reason a block of metal at 10C will feel much colder than a block of wood at 0C.

 

[sgstudent]

What unit of heat is 'N'?

Yes. That's the main reason a block of metal at 10C will feel much colder than a block of wood at 0C.

Sorry it should be J instead. But am i right in the other parts?

 

[haruspex]

Sorry it should be J instead. But am i right in the other parts?

Yes.

 

[NascentOxygen]

So is it possible to have an object with a low heat capacity like alcohol but with an extremely high thermal conductivity such that even when heat is supplied the other end feels cold because it has not reached the 'net' stage.

It is the opposite to what I think you are saying. For a given amount of energy input, the object with lower heat capacity (Joules/degree per kg) will attain a higher temperature, so it will be hotter.

 

[CWatters]

Basically you appear to be asking...

Is it possible to have a material..

...such that even when heat is supplied the other end feels cold because it has not reached the 'net' stage. And only after the heat is transferred to the other end then it will feel hot?

Yes. That's just down to it's thermal condutivity. Compare Gold and Lead rods. Gold conducts heat 10x faster than lead.

But your real question is more complicated...

At first glance the specific Heat Capacity of lead and gold is the same so you might think that the hot end of each rod will start off at exactly the same temperature. However there is a problem. The density of gold and lead aren't exactly the same so rods of the same size will have different mass and the actual heat capacity is different. They will start at different temperatures if you put in the same energy. If you change the size so they have the same thermal mass you mess with the thermal conductivity.

I don't know if there are two materials with the same specific and volumetric heat capacities (but very different thermal conductivity) so that the mass, thermal mass, and volume are the same.

 

[sgstudent]

It is the opposite to what I think you are saying. For a given amount of energy input, the object with lower heat capacity (Joules/degree per kg) will attain a higher temperature, so it will be hotter.

Oh yeah i think i meant high heat capacity and low conductivity. But what does it mean by a block of metal at 10C will feel much colder than a block of wood at 0C?

Does it mean that despite the lower temperature of wood compared to the metal, the greater conductive ability of the metal makes it feel colder?

 

[sgstudent]

Basically you appear to be asking...

Is it possible to have a material..



Yes. That's just down to it's thermal condutivity. Compare Gold and Lead rods. Gold conducts heat 10x faster than lead.

But your real question is more complicated...

At first glance the specific Heat Capacity of lead and gold is the same so you might think that the hot end of each rod will start off at exactly the same temperature. However there is a problem. The density of gold and lead aren't exactly the same so rods of the same size will have different mass and the actual heat capacity is different. They will start at different temperatures if you put in the same energy. If you change the size so they have the same thermal mass you mess with the thermal conductivity.

I don't know if there are two materials with the same specific and volumetric heat capacities (but very different thermal conductivity) so that the mass, thermal mass, and volume are the same.

oh so it's difficult to compare the 2 variables because of the other variables such as density and volume? In the lead and gold scenario, if a fixed amount of thermal energy is supplied to the 2 rod of equal volume and shape then the gold being less dense will become hotter than the lead rod because of a smaller mass (so smaller heat capacity) and will also become hotter faster because it is 10x more conductive so the transfer of heat is faster?

While is the mass is the same for both, then we cannot compare them anymore because the volume and hence shape of both rods will be different due to the difference in density. However, the final temperature will be the same as they have the same heat capacity while we cannot tell which rod will heat up faster due to the shape of the 2 rods being different?

 

[NascentOxygen]

Oh yeah i think i meant high heat capacity and low conductivity. But what does it mean by a block of metal at 10C will feel much colder than a block of wood at 0C?

That was haruspex trying to complicate the issue further.

Does it mean that despite the lower temperature of wood compared to the metal, the greater conductive ability of the metal makes it feel colder?

It relates to the observation that when you handle an object, the more conductive its material then the cooler it feels because it is drawing more heat from your skin in contact. So a steel surface seems colder to the touch than does a plastic surface, even though both have attained equilibrium with ambient temperature. (It would be better, for this test, to compare materials of similar heat capacity but different thermal conductivities. I can't think of any offhand. Perhaps compare the feel of pressing on glass with pressing on a sheet of aluminium?)

 

[CWatters]

oh so it's difficult to compare the 2 variables because of the other variables such as density and volume?

Correct.

While is the mass is the same for both, then we cannot compare them anymore because the volume and hence shape of both rods will be different due to the difference in density.

Correct.

However, the final temperature will be the same as they have the same heat capacity

Correct. If the mass, energy and specific heat capacity are the same then the temperature should end up the same.

while we cannot tell which rod will heat up faster due to the shape of the 2 rods being different?

Correct. Rods of same mass but different density have different volumes. If they are the same length then they are different diameters and that's a factor in the equation for thermal condutivity.