Quartz vs Pyrex Glass Calculations

Intro:

We have been having a lot of discussion within our team and within the scientific community around this effort about the difference between using the quartz glass we currently have the borosilicate (commonly known as Pyrex) that Celani used.  To try to get a better understanding of the trade offs, team member and engineer Nicolas Chauvin performed the detailed modeling of the heat radiation off the wire and the transmittance through the different kinds of glass. Since Quartz glass is more transparent to the infrared wavelengths, our cell could lose a significant amount amount of the heat energy compared to Celanis.  This means we would have to put in more energy to keep the cell at temperature and more heat from any New Fire effect would be radiated away through the glass without making the cell warmer and being detected.  

Nic's Analysis:

Depending on the type of glass we are using for the tube to make the cell, we have realized that we could lose part of the energy through the glass, as some material are transparent to near infrared.

With such potential losses, the Stefan-Boltzmann law would be approximative to calculate the output heat from the cell, as the cell would not behave strictly as a black body.

So we decided to make a little analysis of the amount of power loss we are talking about.
To do this analysis, we developed Excel spread sheet containing the Planck curves from any temperature we want to study.

Then we entered the transmittance of the two types of glass we are currently testing for the cell's tube: Pyrex 7740 borosllicate and fused fused silica (fused quartz). We have compiled the transmittance data for several thickness of glass, thus we will be able to improve the design of the cell by choosing the most appropriate thickness.

By multiplying the power density from Planck's curve with the transmittance of the glass, we can determine the power density kept inside the cell and the loss we have through the glass tube. And we can do this for any temperature inside the cell.

 Here at 560°K (287°C) with a 3.0mm thick borosilicate glass tube:

And here at 700°K (427°C) with a 3.0mm thick fused quartz glass tube:

Finally, by integrating the power density curve over all wavelengths for the standard black body Planck curve and for the one corresponding to our glass cell, we can estimate the percentage of power lost through the glass.
And we can also multiply this integral by the median area of the glass surface to estimate the theoretical power loss through the glass.

For the temperature shown above, at 560°K (287°C) the 3.0mm thick borosilicate tube will have a loss of 1.67% or 3.24 Watts compared to the 3.0mm thick fused quartz tube that will have a loss of 9.42% or 18.31 Watts.
At a higher temperature of 700°K (427°C), the borosilicate tube will have a loss of 5.37% or 25.48 Watts and fused quartz tube 19.00% or 90.15 Watts.

By doing such calculation for different temperatures, we ended with the curves below.

For Pyrex 7740 Borosilicate:

And for the fused quartz:

In conclusion, the fused quartz allows us to achieve much higher temperature, however we would need to increase the thickness to at least 6.0mm to avoid having too much losses we will reduce the precision of our temperature and excess heat measurements.

And we will most probably run some tests with borosilicate tubes at lower temperature (~280°C) to perform a better output heat estimation using Stefan-Boltzmann law.

The Excel files with the full calculation can be accessed here (open the link then download it from File->Download):

• For Borosilicate
• For Fused Quartz

Thanks for reading,

Nicolas