TempMeter : Measuring Temperature with a Brass Rod

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For the Proving Science Project14 activity I thought I would have a go at measuring temperature using a technique I remember being discussed when I was at school, originated by a fellow pupil rather than the teacher, but not actually seen in action. It was in a physics class looking at the expansion of materials with temperature and it was a mind-changing moment for me as I realised that science and engineering stuff was so exciting and anyone could think about stuff and not just teachers and old people. I like thinking about stuff and often do it in the garden sitting in the sun with my eyes closed.

The method works by using the expansion coefficient of a metal. A metal with a good expansion coefficient is brass (11 x  10 ⁻⁶   F ⁻¹   ) and I just happen to have some brass rod (for the Art Project14 competition). Aluminium is better at 13 x 10 ⁻⁶ F ⁻¹   but I do not have Aluminium rod so brass it is. I will be using Fahrenheit rather than Celsius as I have a digital temperature meter and this provides slightly better resolution. I am using a 30 cm rod of 2.0 mm rod as the expansion length which rests on a 1.0 mm brass rod. As the long rod expands and contracts due to temperature the smaller brass rod will act as a roller and rotate forwards and backwards as well. By placing a pointer on the 1.0 mm roller rod I will obtain an indication of temperature.

As all (?) materials expand with temperature this means the base will as well so I need a base with the lowest expansion coefficient I can find. Diamond seems to be the lowest but as I do not have a sheet of diamond to hand I have decided to use reconstituted stone from an old fire place. It should be somewhere between brick (about 3) and marble (about 6). Plus, it is very straight and very smooth and shiny so the roller should move freely. I gave the surface a good clean (wiped with a damp cloth - that's clean enough!) and clamped a piece of wood at one end as a stop for the brass rod - using a blob of Blue-Tac to just hold it in place. In order to get some friction on the roller I used a flat steel ruler as a weight place near the roller. This will affect the rolling but it will be of minimal impact - hopefully.

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TempMeter : Measuring Temperature with a Brass Rod

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For a brass rod of length L = 300mm having an expansion coefficient of e = 11 x  10 ⁻⁶   F ⁻¹   then a 1 degree Fahrenheit increase ( δ T = 1) in temperature will lead to an increase in the rod length of:

  δ L =  L x e  x  δ T

          = 300 x 11 x  10  ⁻⁶  x 1  mm

          = 3.3 x 10 ⁻³   mm

The smaller brass rod used as a roller has a diameter of d =1.0 mm giving it a circumference of:

C = d π .

    =   π    mm π

The angle turned through due to the expansion is:

θ   =  δLdπ x 360  degrees

So a 1 degree increase in temperature in Fahrenheit will lead to a change in angle of :

θ  = ( 3.3 x 10 ⁻³  x 360) /  π    degrees

     = 0.38 degrees

The clock face has 12 hour divisions with 5 minute divisions in each hour totalling 60 divisions for the full clock face. Therefore 1 division represents an angle of 360/60 = 6 degrees. So a 20 increase in temperature will lead to (20 x 0.38 ) 7.6 degree change in angle which is just over one increment on the dial. I would have to say that this is not going to be that useful. Still, the technique does work but might need some refinement.

A longer brass rod would help, as would a thinner roller, maybe a needle or a pin. It is a fairly hot day today so if tonight is cooler, maybe a change of 20 F then it may be possible to see the rotation on the dial. If it happens I will amend this blog to include it. Otherwise I will have to wait for a much colder day, which could be several days!

Dubbie