Principles
And Construction 2b:
Tech: Heat Capacity
Heat Capacity
Specific heat capacity is a way of describing the amount of energy required to heat a given amount of substance, such as the mass of a wall, through a certain change of temperature. When you warm the substance, you must put heat energy into it. When you cool the mass, you must remove heat energy from it.
How does this actually work? Supposing you wanted to increase the amount of energy you could store in a mass. One way to do that would be to increase the actual amount of mass on hand. Another would be to increase the change in temperature the mass goes through. So, therefore, heat capacity must be measured in units that include a change in temperature, an amount of energy, and also an amount of mass.
Specific heat capacity is measured in joules per kilogram kelvin (J/kg·K).
In looking for information about thermal mass on the internet, you'll also find mention of the volumetric heat capacity of substances, measured in joules per cubic metre kelvin (J/m3·K). If you know the mass density of the substance, in, for example, kilograms per cubic metre (kg/m3), you can use that to convert to and from the specific heat capacity.
Specific heat capacity and volumetric heat capacity have been measured for various building materials. Concrete, for instance, has a specific heat capacity of 880 J/kg·K, a volumetric heat capacity of 2060 kJ/m3·K and a mass density of 2250 kg/m3.
But how does this help with finding out how much heat can be stored in the walls of the house?
From looking at the plans, and taking into account the thicknesses of the walls, and what they are constructed of, you can find out how much mass is in the walls. By using the specific heat capacity, and postulating a change in temperature, you can figure out how much heat energy would be stored in your walls with each degree rise in temperature, and how much heat energy would be released with each degree fall.
Let me demonstrate...
Let's say you had a concrete wall 50 cm thick, three metres high, and 6 metres long. That's 0.5 m x 3 m x 6 m. The total volume of concrete in the wall is therefore 0.5 m x 3 m x 6 m = 9 m3 (width x length x height).
Let's also say you are raising its temperature by 10 degrees Celsius. That's a temperature difference of 10 kelvins.
Since the volumetric heat capacity of concrete is 2060 kJ/m3·K, the amount of energy put in to the wall to raise its temperature by 10 K is 2060 kJ/m3·K x 9 m3 x 10 K, or 185 400 kJ (185 400 000 J).
A hundred and eighty-five million joules. That's just a number. But, searching around on the internet, I found that a cubic metre of natural gas, when burned, yields 37.5 million joules of energy. According to Enbridge, the gas company in Southern Ontario, that gas also costs 48.8 cents per cubic metre.
So, to warm that wall by 10 K (or 10 Celsius degrees--same thing) using natural gas would take a minimum of 185 400 000 J / 37 500 000 J/m3 = 4.95 m3 of gas. And that gas would cost $2.41.
And that's assuming everything works perfectly, the furnace works perfectly, and all the heat goes into the wall.
And consider this: that's a small wall. The walls of the Potters' house are much larger, a hundred times the volume, containing much more concrete and rammed earth. So we're talking about, potentially, a charge of several hundred dollars to warm them by 10 degrees.
And during the winter, there is often a temperature of -30 degrees Celsius outside. So to warm the walls to room temperature, they would have to warm through 50 degrees Celsius (or 50 K). Now how much would they pay to warm them? And keep paying, as the walls cooled off again?
Fortunately, there is another way. We use the sun to warm the walls, and we insulate them to keep the heat from leaking away.
Next: heat conduction, or, "how does this insulation thing work, anyways?" --in which I describe where the "R-value" splattered on packages of insulation comes from.
References:
Wikipedia on specific heat capacity. The values here are given in J/g·K, not J/kg·K, which goes to show that even in the metric would, things can get confusing. But 1 J/g·K = 1000 J/kg·K.
An Australian government site on thermal mass. This page gives volumetric heat capacities and densities for a variety of building materials.
I also got information from Building Science for a Cold Climate (Table 8.1, page 161.)
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