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I'm currently working on a science experiment to find out whether the thickness of a material affects the insulator's ability to insulate, and if so, to what extent.

I've set up an experiment where I put a sheet/layer of an insulator on top of a light box, and a polystyrene cup with a thermometer placed inside to see how much heat transfers to the polystyrene cup. The purpose of this set up is to mimic house insulation, where the lighting box is the house, and the polystyrene is the roof. I repeated this for 4 different layers.

I measured the temperature inside every 2 mins for 20 minutes. I repeated this for 4 different layers.

Therefore, I would like to know if there's an equation that could use both change in time and change in temperature to find whether the insulator is effective or not.

I have thought of using the equation

but, I cannot really calculate the Heat Loss without the r-value.

I've also thought of using the equation for heat transfer, but I am not sure whether heat transfer is a good equation to use for checking the material's ability to insulate. Furthermore, I have not measured the temperature of the light box, but instead just the starting temperature of the polystyrene cup. Therefore, I wouldn't be really able to use it.

I also cannot use r-values off the internet, as the insulators I use does not have a r-value.

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The heat transfer equation is the only tool you have to work with. It relates the rate of heat-flow $\dot Q$ through the material to the temperature difference across it : $$\dot Q=\frac{dQ}{dt}=-\frac{A}{RL}(T-T_0)$$ where $A$ is area, $L$ is thickness and $R$ is R-value of material, $T$ is the varying temperature inside the "house" and $T_0$ is the constant "outside" temperature. The minus sign indicates that heat is flowing in the direction in which temperature is decreasing.

If the heat capacity of the house is $C$ and the temperature in the "house" is uniform then $Q=C(T-T_0)$. We can substitute for $Q$ and integrate to get $$t=L\frac{RC}{A}\ln[\frac{T_1-T_0}{T-T_0}]=a-b\ln(T-T_0)$$ where $\ln$ is the natural logarithm, $T_1$ is the starting temperature inside and $T_0$ is the lowest finishing temperature - ie the temperature outside. In your experiment $T_0$ is the laboratory temperature, which you will need to measure or estimate from your data.

For each thickness $L$ plot a graph of time against $\ln(T-T_0)$. This graph should be a straight line sloping down to the right. Measure the slope $b$. Then plot a final graph of slope $b$ vs thickness $L$. The slope of this graph will not be very meaningful but if this graph is a straight line it shows that rate of heat loss is inversely proportional to thickness of insulator, as assumed in the heat transfer equation.

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