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Heat Capacity; What it is.


SteamyTea

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Heat capacity is a really simple concept, confusion comes about because it get mangled beyond belief.

Some of this mangling is actually physical i.e. we change the shape of a heated object, and other mangling is with words i.e. not knowing much about the subject.

 

I like to stick with the physical, it is easy and, more importantly, you can put descriptive units to it.

 

To start with, let us look at the two types of heat capacity.

 

Specific Heat Capacity

 

Specific Heat Capacity (cp, SHC) is based on the mass of the material and how much energy (J, joule) it takes to change the temperature by 1 K (kelvin).

This make for very eas-3y to understand units, but can cause confusion because it is often assumed that the temperature, K, is the important part of the formula and has to be what governs the amount of energy that all materials can store.

 

J.kg-1.K-1

 

Different materials have different SHCs and at first sight do not seem to make much sense.

Air has a higher SHC than granite, and water can experience 3 different SHC in one day.

 

Air = 1.012 kJ.kg-1.K-1 

Granite = 7.10 kJ.kg-1.K-1 

 

Timbers can be very confusing

 

White Pine = 2.5 kJ.kg-1.K-1 

Oak = 2 kJ.kg-1.K-1 

Balsa = 2.9 kJ.kg-1.K-1 

 

Water(steam 372K) = 2.03 kJ.kg-1.K-1 

Water (liquid 298K) = 4.18 kJ.kg-1.K-1 

Water(ice 263K) = 2.05 kJ.kg-1.K-1 

 

The reason that water, and most materials for that matter, has 3 different SHC is because it changes phase and during that change, the energy absorbed or released can be huge.

 

 

Volumetric Heat 

 

This is based on the volume and is usually the more useful unit (cvcpv, VHC) to use and has the formula

 

J.m-3.K-1 

 

It is just the product of the SHC and material density (ρ, Rho, D).  Density is the mass of a material by unit volume, kg.m-3 

 

Taking typical London brick as an example.

 

c = cp x ρ 

 

cpv(brick) = 0.84 [kJ.kg-1.K-1] x 1845 [kg.m-3]

 

c = 1,550 kJ.m-3.K-1 

 

As an ordinary London Brick is 0.215m x 0.103m x 0.065m and ignoring the mortar mix (cp = 0.96 kJ.kg-1.K-1ρ = 2080 kg.m-3), an area of 1 m2 will take approximately 155 kJ to change in temperature by 1 K.

Depending on the starting conditions i.e. the outside and inside air temperatures, the mean starting temperature of the brick, the thermal conductivity and the time taken to change, the thermal conditions change that 155 kJ number because of the thermal conduction losses.

 

That is it really, the main things to remember, to save confusion, is that one must specify which heat capacity is being used i.e. by mass or volume, are any phase changes happening i.e. plaster drying out, and make sure the units are shown.

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Thanks for posting this @SteamyTea , I struggle with stuff like this, so - for me - this a useful first step.

 

I like to start stuff with a clear end in mind. For me that would be a clear idea of why I need to know about the Heat Capacity of (say) a tank of water? What does knowing that measure give me to assist my thinking about the tank of water

 

Once I know that, the next issue is - which of the two measures (Volumetric or Specific) should I use ? And more importantly, once one is chosen, what is the rationale for  not   using the other measure ?

 

Or maybe - is there a simple rule when it is better to  one and not the other?

Thanks anyway

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38 minutes ago, ToughButterCup said:

What does knowing that measure give me to assist my thinking about the tank of water

It gives you the information to compare with other storage systems.

 

39 minutes ago, ToughButterCup said:

which of the two measures (Volumetric or Specific) should I use ? And more importantly, once one is chosen, what is the rationale for  not   using the other measure ?

This comes down to context.

I tend to use SHC as I can think better in mass than volume, all mass is equal. Heat capacity depends on material density, so varies, a m3 of timber is physically larger than the same volume of stone.

Sometimes you just have to pick the most appropriate unit.

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15 minutes ago, SteamyTea said:

Heat capacity depends on material density, so varies, a m3 of timber is physically larger than the same volume of stone.

Is that what you really meant to say as it reads somewhat like the old which is heavier a kg of bricks or a kg of feathers josh🤔

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14 minutes ago, MikeSharp01 said:

Is that what you really meant to say as it reads somewhat like the old which is heavier a kg of bricks or a kg of feathers josh🤔

Your dead right, I was eating a kebab while watching the sun set.

 

Timber has a lower density, so larger volume for the same mass.

 

Does highlight why it is not a good idea to mix units, until the very end.

Edited by SteamyTea
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15 hours ago, SteamyTea said:

It gives you the information to compare with other storage systems.

 

This comes down to context.

I tend to use SHC as  [...]  Sometimes you just have to pick the most appropriate unit.

 

Ah yes, Context - always important: as In   Danger! No Swimming Allowed!  OR  Danger? No, swimming allowed.

 

The difference - either an exclamation mark or  a question mark - is used to match the context.

Here swimming is fine - but don't swim there.

 

The person putting up the correct sign knows how to read the context. Because of thousands of things in my life experience, in terms of swimming, I can make a good guess about which sign to display. But I'm clueless about heat capacity 

 

Can you (or anyone) start me off by giving a short simple list of  contexts and the most appropriate measure for those contexts please? Thanks.

 

For example ;

How about - choosing a hot water tank .... or comparing SunAmp 'batteries'  .... or  storage heaters ...  or a kettle (?)

I'm not even confident that I'm asking the correct question - if so tell me.

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4 hours ago, ToughButterCup said:

How about - choosing a hot water tank .... or comparing SunAmp 'batteries'  .... or  storage heaters

This is quite difficult, but only because it is laborious.

I made a matrix of some common properties of a water cylinder, a Sunamp and a storage heater, all with a similar nameplate thermal capacity.

I converted the values into rated capacity in kWh, cubic metres, litres/minute flowrates, input power, dimensions, volumes, mass, standing losses (though not relevant for a storage heater), kWh/m3.K and kWh/kg.K, floor loading and recharge times.

 

Then it is just a matter of picking from the lists the properties that best suit the installation i.e. floor area, height etc.

I have not put any prices in as they are way to variable and very specific to the installation i.e. pipe runs, cabling, floor reinforcement.

 

A quick not on a storage heater.  These work by loosing heat at a controlled rate, which is why the numbers look a bit strange.  I made an assumption that there are no losses during the recharge period (even though this is not true in practice, but more closely matched the way water storage is measured), then worked out an equivalent amount of water storage (the Equivalent Storage /lt row), which was divided by 17 hours discharge time, then converted to litres per minute.

This is not really a fair comparison and only really relevant for water delivery.

Another way to look at it is to divide the storage capacity by 17 hours (the usage period) and get a kW delivery (they are all pretty similar).

 

The biggest problem is know what temperature difference to use, so I picked 35K for water storage (maxing out at 65°C), 5K for the Sunamp (delivery is 40° after all) and 45K for the storage heater (the bricks get very hot).  These numbers are very much open to debate and are really, in this instance, something to work to.  They can be adjusted.

 

Properties Water Cylinder (Kingspan 250 lt AU12250ERP)   Sunamp (Thermino 210e)   Storage Heater (Creda TSR12)
Input kW 6   2.8   1.7
Height m 1.744   0.87   0.705
Diameter/Width m 0.55   0.365   0.56
Depth m     0.757   0.17
Mass kg 305   178   77
Equivalent Capacity lt 250   210   208
Standing Losses W 84   32   N/A
Flow Rate lt/min 12.5   20   0.01
Rated Capacity 10.2   10.5   11.9
Power kW 0.60   0.62   0.70
Volume m3 0.91   0.24   0.07
kWh/m3.K 0.317   8.736   3.940
kWh/kg.K 0.001   0.003   0.001
Floor Loading kN/m2 5.7   6.3   7.9
Recharge Times /h 1.7   3.8   7.0

 

4 hours ago, ToughButterCup said:

or a kettle

A kettle is a good thing to play with.  You can easily check the input power, it is written on the base, easy to put different amount of water in, what a Pyrex jug is for, the starting and ending temperatures will be the same (run the cold tap for a few seconds first) and then time the time to boiling.

If you want to get a much better feel for what heat capacity is, every 10 minutes after boiling take some water temperature readings, then plot them.  It won't be a straight line.  Will be, roughly, 3 times longer for every 10K temperature drop.  Actually {\displaystyle T(t)=T_{\text{env}}+(T(0)-T_{\text{env}})e^{-rt}.}

 

 

 

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Thanks very much indeed  @SteamyTea

 

This bit clicked

Quote

If you want to get a much better feel for what heat capacity is, every 10 minutes after boiling take some water temperature readings, then plot them.  It won't be a straight line.  Will be, roughly, 3 times longer for every 10K temperature drop.

 

10K is 10 degrees Kelvin isn't it - I hope (?)  And I conclude - hesitantly - that water releases its heat to the environment in a non-linear way . It releases its heat more quickly at first, and as the (its) temperature drops, the heat is released more slowly.  

 

The thing that gets me is the term in this context is  'specific'  Is the word 'specific' used  in this context as - specific to water ?   Specific because water will (or any material will) release its heat to the atmosphere at a rate specific to that material ? As below from your first post above

 

Quote

Specific Heat Capacity (cp, SHC) is based on the mass of the material and how much energy (J, joule) it takes to change the temperature by 1 K (kelvin).

 

In the example you give (of water from a kettle cooling down) the water will be giving up its specific heat  more slowly the cooler it gets because as the water cools, it has less specific heat (energy) to radiate(?) to the atmosphere ?

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31 minutes ago, ToughButterCup said:

10K is 10 degrees Kelvin isn't it

Yes, why it is a big K for kelvin.

32 minutes ago, ToughButterCup said:

The thing that gets me is the term in this context is  'specific'  Is the word 'specific' used  in this context as - specific to water

No.  Specific means by mass, kg, small k as it is 1000.  Every material will have a different specific heat capacity and it is not based on material type i.e. gas, liquid, solid, density shape, metallic, non metallic, natural or man made, pure or alloy etc, and just to make it worse, most materials will vary the SHC with temperature and what phase they are in i.e. gas to liquid.  This is also known as sensible heat.  Wedged in between phases, the place where the state changes, but the temperature remains the same, will also have a different heat specific heat capacity, this one is called latent heat.

 

39 minutes ago, ToughButterCup said:

In the example you give (of water from a kettle cooling down) the water will be giving up its specific heat  more slowly the cooler it gets because as the water cools, it has less specific heat (energy) to radiate(?) to the atmosphere ?

Basically yes, when half the energy has gone, there is only half of the original to loose.

This is where shape comes in, and is why surface area is important.  The larger the surface area, the faster the energy can be lost, why we have large surface area radiators with low temperature systems.

What is really happening is that it is giving up its sensible heat, specific heat is basically fixed.

Heat is only the old word for energy and has nothing to do with temperature.  This often causes confusion, just remember, if you see the word heat, replace it with the word energy, and see if it makes sense, if it does not, then replace it with temperature.

 

I tend to think in terms of energy and power for most thermodynamic 'things'.  All that means is how much of something do I have to play with, and how fast, or slow, can I get rid of it.  Bit like budgeting at the end of the month when you know you have a bill or two to pay.

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I have just noticed that I made an error in working out the volume of the water cylinder, this changes the heat capacity to 0.701, which is over double the 0.301 I originally posted.

So that line is now.

 

Properties Water Cylinder (Kingspan 250 lt AU12250ERP)   Sunamp (Thermino 210e)   Storage Heater (Creda TSR12)
           
kWh/m3.K 0.701   8.736   3.940
           

 

 

Still looks pretty poor in comparison but that cylinder has the expansion chamber built it, so it bigger than it needs to be to hold 250 litres of water.

If it was just the water, then the volume would be 0.35 m3 rather than the 0.41 m3 that it works out as with the expansion vessel and insulation.

 

Floor loading becomes 12.6 kN/m2 as well.

Edited by SteamyTea
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