# Calculating R-value from temperature differential

A home windows installation rep gave me a quote today and conducted the following temperature differential demonstration.

1. Alice pointed a heat gun (with a surface temperature of 165F) at the interior surface of a window.

2. Bob measured the exterior surface of the window (with a no-contact laser thermometer) to be 45F.

Is there any way to calculate R-value (or any other standard thermal insulation reference) given the temperature differentials resulting from the above setup and procedure? Can the setup or procedure be improved in order to get an R-value or any other standard and useful benchmark or metric? If so, how?

Fig. 1. Test Setup

Edit: Per one of the answers, let's make the simplifying assumption the temperature of the window's interior surface is equal to the temperature of the heat gun.

• What are the units of R? That should tell you what to what to think of... – Solar Mike Dec 15 '17 at 6:50
• the main essential thing missing here to even get an approximate result is the outside air temperature. – agentp Dec 15 '17 at 22:34
• In order to calculate the thermal resistance you need to know the temperature drop across the window, and the heat transfer rate through the window. Since you don't know the heat rate, you can't calculate the R factor. There's not enough information. – Mark Dec 17 '17 at 0:49

There are a lot of things wrong with the demonstration, including:

1. The temperature of the heat gun isn’t relevant - to measure the R value you need to look at the temperature difference across the window, not from the heat gun to the far side of the window. Kind of like calculating the heat loss through your walls based on the outside temperature and the temperature in your fireplace.
2. A lot of the heat loss through windows is through the frame rather than through the glass. Window energy ratings typically include an overall value, and a glazing-only value.
3. Heat loss has to be measured under steady-state conditions using a test setup that measures temperatures and heat transfer.
4. The relevant equation is Q = U A DT where Q is heat flow, U is the overall heat transfer coefficient (1/R), A is the area, and DT is the temperature difference. To measure R or U, you have to know both of the temperatures and the heat flow.

In the end though, you really don’t need to do all this. The windows should have a label that provides a U value which you can compare to other windows, or use to calculate the R value. See here for more information

Borrowing from this answer (and its associated question): You must factor in the time you are taking the measurement as well as the starting temperature of the window.

The temperature change over time for different materials looks like the following

Material 3 has the highest R-value and 1 has the lowest. R-value is proportional to the inverse of thermal conductivity, $k$

$R \propto \frac{1}{k}$

The relevant heat-transfer equation is as follows:

$\dot{Q} = k A \frac{\Delta T}{l}$

where,

$l$ is thickness

$A$ is surface area

From this follows that besides other factors the rate of heatflow is proportional to the thermal conductivity, $k$.

$\dot{Q} \propto k$

therefore,

$R \propto ln(\frac{\Delta t}{\Delta T})$

where $\Delta t$ is the length of time the heat lamp was on the window prior to the temperature measurement reading.

• So does your answer respond to the original question? – Solar Mike Dec 15 '17 at 19:05
• @SolarMike: Partially. But not fully. It's worth noting this answer says the R-value can not be calculated with the given information. Specifically, we need to know $\Delta t$. This answer can definitely be improved by giving a more explicit mathematical relationship. However, I feel this answer as it currently stands isolates the variables critical to determining the explicit equation the OP requests. Please feel free to improve upon the answer with more detailed math or references if you wish. – Mowzer Dec 15 '17 at 20:17
• I don't see the text "the R-value can not be calculated.." in your answer... – Solar Mike Dec 15 '17 at 20:21
• @SolarMike: The first sentence says: "You must factor in the time you are taking the measurement as well as the starting temperature of the window." Neither of which is given in the OP. – Mowzer Dec 15 '17 at 20:23
• The R value is not just 1/k, it’s 1/U where U is the overall heat transfer rate which includes the k factor as well as the internal and external convection factors. To measure the U or R value you have to know the interior and exterior temperatures as well as the heat transfer rate, Q. These equations don’t really address the question. – Mark Dec 15 '17 at 20:27