Re: [Phys-l] heat loads, was Insulation R-values

[Ludwik Kowalski <kowalskil@mail.montclair.edu>]

On Feb 17, 2006, at 10:31 PM, jbellina wrote:

> I'm not sure what you want...do you mean the average thermal
> conductivity of your house?  You could I suppose turn off the heat
> and track the interior temperature as function of time.  That should
> be an exponential decrease in temperature with the conductivity in
> the exponent, so if you did the proper linearization you could
> extract the product of the conductivity and the geometric factors
> like area and wall thickness.

That is another method to determining the coefficient of conductivity. 
Here is how I would implement it by using a box with a lamp, as 
suggested by Mike. That box, with a thermometer inserted, is suspended 
in still air whose temperature is constant.

a) Start when the temperature inside is the same as the temperature 
outside, for example, 20 C. Turn the electric power on and wait for a 
desired temperature, for example, 50 C.
b) Knowing the time it takes, and the power of the heater, calculate 
the amount of heat, Q, received by the box. For example, Q=12,000 J 
when P=40 W and time is 300 s
c) Knowing the mass of the box, for example, m=2 kg, calculate its heat 
capacity, K, for example, K=12,000/2=6000 joules per degree C.
d) Start collecting data for the cooling curve. Suppose that the 
temperature is 32 C at t=1000 s and 28 C at t=1600 s.
e) How much heat was lost in 600 s? It is K*4=24,000 J. Use this to 
calculate H=24,000/(2*10)= 1200 J/(m^2^C). I am assuming that the area 
of the box is 2 m^2, and that the temperature inside the box is 30 C.
f) Knowing H calculate k from its definition (H=k*dt/d), as described 
yesterday. Or define R and calculate it from your own definition.

Textbooks tell us that H, in the definition of k, refers to conductive 
losses only. My definition of R, in a market situation, would be in 
terms of total losses. Why? Because consumers are likely to be 
interested in total loses only. Also because measuring the total H is 
much easier that measuring only one part of it.

Does convection play a significant role when a box has no holes? 
Suppose it is windy outside. Wind is a form of convection. With wind 
the outer surface of each wall has the same temperature as cold air. 
Without the wind the situation might be more complicated because the 
outer surface of the wall might not have the same temperature as cold 
air. The temperature might be, for example,  21 C when the cold air 
temperature is 20 C. That is why, at least in principle, conditions 
under which R is measured should be part of its definition.

Ludwik Kowalski
Let the perfect not be the enemy of the good.