Specific Heat Capacity of solids liquid or Gas, which is largest?

[matthew77ask]

This questions puzzles me:

Which has a larger specific heat capacity (shc) : solid, liquid or gas.
We can assume that it is of the same matter. Why?

I have checked the numbers. Only water has it on all three states. Liq water has the highest, while that of ice and steam is about the same.

We are not talking about thermal conductivity here. If we are then kinetic particle theory will point to solid > Liq> Gas in thermal conductivity because of the closer solid particles can "pass" on the heat fastest compared to the further gas particles.

Can the same theory applies when it comes to shc? the amount of heat needed to raised the temp by 1 degree C? if it can then the order would be shc of gas > liq > solid. But this is not the case for water...

Is SHC of a matter a function of the matter itself rather than the closeness of the particle.

Sorry, fired up a lot of questions... hope someone can enlighten me and take some heat away


Cheers!
Matthew

 

[Andrew Mason]

This questions puzzles me:

Which has a larger specific heat capacity (shc) : solid, liquid or gas.
We can assume that it is of the same matter. Why?

I have checked the numbers. Only water has it on all three states. Liq water has the highest, while that of ice and steam is about the same.

We are not talking about thermal conductivity here. If we are then kinetic particle theory will point to solid > Liq> Gas in thermal conductivity because of the closer solid particles can "pass" on the heat fastest compared to the further gas particles.

Temperature is the measure of the average kinetic energy of the molecules. In ice, the energy added results in increased vibrational energy of the water molecules (all kinetic). In steam, added energy results in increased translational, vibrational and rotational energy (all kinetic). In liquid water, however, not all of the added energy results in kinetic energy of the molecules. Can you think why this would be? (think of bonds between water molecules).

AM

 

[matthew77ask]

Temperature is the measure of the average kinetic energy of the molecules. In ice, the energy added results in increased vibrational energy of the water molecules (all kinetic). In steam, added energy results in increased translational, vibrational and rotational energy (all kinetic). In liquid water, however, not all of the added energy results in kinetic energy of the molecules. Can you think why this would be? (think of bonds between water molecules).

AM

If I understanding this correctly:

In solids (eg ice) heat will cause the avg ke (vibration at fixed location)of the molecules to increase faster cos they are closely pack. So a small amount of heat energy (Joules) will be enough to raise the temp by 1 C.

In gases (eg steam) although the dist between the molecules are far, the heat energy increases the movement of the molecules (as in molecules will move about faster) and hence pass the heat energy around by banging each other (the small bangs theory fly and bang ). Hence small amount of heat energy will be enough to raise the temp by 1 C.

In liquids (eg water), however, the molecules are neither very closely pack (so that heat can pass by juz pure vibration) nor very far apart (so heat can pass via flying around and banging others). The molecules in liquid are bonded by van der waals forces and some other forces (eg H-bond). So the movements are very restricted compared to gases, and heat energy cannot be passed via the fly and bang method. Nor heat can pass quickly by vibrating and passing the heat to your next door neighbour as in the case of solids. So a larger amount of heat energy is needed to raise the temp by 1C.

Am I correct so far?


Thanks

 

[Astronuc]

All substances have a specific heat in solid, liquid or gas. Water is just rather ubiquitous.

One has to consider not only the atomic/molecular mass, but the structure, e.g. elemental vs molecular/chemical.

See - http://en.wikipedia.org/wiki/Specific_heat_capacity - explanation and table.

http://hyperphysics.phy-astr.gsu.edu/hbase/tables/sphtt.html#c1 - table of specific heats.
http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/dulong.html

http://hyperphysics.phy-astr.gsu.edu/hbase/kinetic/shegas.html - gases

http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/phase.html - water and phase change

 

[Andrew Mason]

If I understanding this correctly:

In solids (eg ice) heat will cause the avg ke (vibration at fixed location)of the molecules to increase faster cos they are closely pack. So a small amount of heat energy (Joules) will be enough to raise the temp by 1 C.

In gases (eg steam) although the dist between the molecules are far, the heat energy increases the movement of the molecules (as in molecules will move about faster) and hence pass the heat energy around by banging each other (the small bangs theory fly and bang ). Hence small amount of heat energy will be enough to raise the temp by 1 C.

In liquids (eg water), however, the molecules are neither very closely pack (so that heat can pass by juz pure vibration) nor very far apart (so heat can pass via flying around and banging others). The molecules in liquid are bonded by van der waals forces and some other forces (eg H-bond). So the movements are very restricted compared to gases, and heat energy cannot be passed via the fly and bang method. Nor heat can pass quickly by vibrating and passing the heat to your next door neighbour as in the case of solids. So a larger amount of heat energy is needed to raise the temp by 1C.

Am I correct so far?

Not quite. But you are thinking. This is a good question and it is not an easy one to figure out. The physics of water, which is a polar molecule, is complicated.

But here are are few comments.

Heat is energy. Heat 'passes' due to molecular collisions. Temperature is the measure of molecular kinetic energy, not heat. So, if more heat is needed to raise the temperature of a mole of liquid water one degree than a mole of steam one degree, this means that some of that heat energy is not going into kinetic energy of the liquid water molecules. So what is it going into? It must be going into breaking the hydrogen bonds that water molecules form with each other. This does not happen in ice or steam, since those bonds are not being broken or are already broken. The warmer the water, the more vapour molecules there are breaking those hydrogen bonds (and escaping from the surface). This is why water vapour pressure increases with temperature.

AM

 

[matthew77ask]

Thanks AM, not sure if I comprehen it fully.

I think I may be using the 'wrong' example - water. because of it's nature.

But in other matter - would SHC of solid > liq > gas or other way round. Or is there a pattern at all?

cheers!

 

[Andrew Mason]

Thanks AM, not sure if I comprehen it fully.

I think I may be using the 'wrong' example - water. because of it's nature.

But in other matter - would SHC of solid > liq > gas or other way round. Or is there a pattern at all?

cheers!

It depends on the bonds between the molecules in the liquid. If the bonds are realtively stong hydrogen bonds (such as in water), a lot of the heat energy will be used in breaking those bonds, so the liquid will have a higher heat capacity. If the molecular bonds are weak (eg. Vanderwaals forces) not much heat will be used. So the heat capacities of liquid metals will not be much different than the heat capacities of the solid metals.

AM

 

[BLG]

AM:
'''' If the bonds are realtively stong hydrogen bonds (such as in water), a lot of the heat energy will be used in breaking those bonds, so the liquid will have a higher heat capacity ''''

Hi AM,

According to your quote above, a higher cp is because bonds are constantly being formed or broken. However, bonds are formed only at the melting/evaporating points, and not throughout the sensible heating of the liquid form.
I believe it depends on the energy balance between the kinetic energy (all forms: translational, vibrational & rotational) and the inter-molecular potential energy. As the molecular structure becomes looser in a liquid from a solid, the molecules are more free to move, but restricted by the intermolecular forces. Hence the heat input is used for the kinetic energy (all types - compared to only vibrational for solids) but also as work against the intermolecular forces. Work against the bonds does not mean breaking them, but if you want 'stretching' them. When the melting temp is reached, the kinetic energy has reached its apex in the liquid form, and all energy is used to only break the intermolecular bonds = melting.

Hope this helps...
BLG