# Heat Capacity; What it is.

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 (*c _{p}*, 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 (*c _{v}, *

*c*

*, VHC) to use and has the formula*

_{pv}

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* = *c _{p}* x

*ρ*

*c*_{pv}_{(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 (*c _{p}* = 0.96 kJ.kg

^{-1}.K

^{-1},

*ρ*= 2080 kg.m

^{-3}), an area of 1 m

^{2}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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