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An Elastocaloric Calorimeter

January 13, 2020

I've always enjoyed doing simple benchtop experiments, especially those that can be assembled from household items (at least in my high-tech household with an electronics workshop). There might be some nostalgia in this, since I spent my childhood working on one science fair experiment after another.

Physicist and Nobel Laureate, Ernest Rutherford (1871-1937), was famous for building experiments from common articles such a piece of a bicycle handlebar, string, and sealing wax.[1] The official cost of construction of the Large Hadron Collider, including research and development, testing, and pre-operation, was nearly $5 billion, and this is probably a conservative estimate.[2] You can buy a lot of test tubes and pan balances for that amount of money.

Ernest Rutherford-1908

Although Ernest Rutherford (1871-1937) was a physicist, he was awarded the 1908 Nobel Prize in Chemistry. This must have reinforced his belief that serious science is all physics.

Rutherford is famous for the discovery of the proton, and as Director of the Cavendish Laboratory of Cambridge University in 1932 when James Chadwick discovered the neutron.

While not much string and sealing wax are used in today's laboratories, they've been replaced by items such as WD-40, super glue, and my favorite, five-minute epoxy.

(Wikimedia Commons image, modified for artistic effect.)


In the previous article (Elastocaloric Effect, November XX, 2020), I described recent experiments on the elastocaloric effect in which rubber releases heat when stretched, and then absorbs heat when allowed to relax. This is a manifestation of a change in the material entropy caused by changes in the alignment of molecules. Since I've had experience in calorimetry,[3] I decided to assemble a simple elastocaloric calorimeter using materials available in my home workshop. Numbers are one thing, but I didn't realize how small this effect was until I did some experiments.

The layout of my calorimeter is shown in the figure. The inner and outer cylindrical containers were made from vitamin and dietary supplement containers of appropriate sizes. To enhance sensitivity, I made the water bath that receives heat from the stretched rubber bands as small as possible. A simple mechanism allows twisting the rubber band by rotation at the top against a fixture at the bottom. A motorized stirer is used to uniformly transfer heat to the water bath, and a resistor is placed for calibration by passage of an electric current for a set time. The photograph gives detail of the construction.

Calorimeter layout

Calorimeter layout. The inner container sits on a sheet of Styrofoam, while fiberglass is used as the remainder of the insulation material. There's a mechanism that holds the twist knob in place when the desired number of turns is reached. (Created using Inkscape. Click for larger image.)


Photograph of the calorimeter.

Photograph of the calorimeter, and a detail view of the interior components. In this case, a Buna-N O-ring is mounted on the torsion assembly. Since it's always desirable to minimize heat leakage to the environment, the calibration resistor and temperature sensor are suspended on thin wooden rods, and the stirer is Delrin. Unfortunately, mechanical strength is needed in the twist assembly, so quarter-inch diameter aluminum rods are used. (Click for larger image.)


Some of my experiments in the 1970s involved sitting in front of an analog voltmeter and taking data in a laboratory notebook. Computers have made data acquisition much easier, and I have a 12-bit analog-to-digital converter that attaches to a computer serial port. I realized that I needed more resolution than 12-bits could provide, so I built a circuit, shown below, that amplifies the signal from a semiconductor temperature sensor by a factor of ten to give an effective 15-bit resolution. One caveat of the circuit is that the rail-to-rail operational amplifiers function well only in their mid-range, so I "zeroed" the differential signal at mid-range and not at zero volts. Offset and calibration were handled by software.

Calorimeter circuit

Calorimeter circuit. The LM335Z is a convenient temperature sensor, and it has an output voltage that's proportional to the absolute temperature. (Click for larger image.)


In my experiments, the calorimeter was calibrated by application of ten volts to a 50 ohm resistor for one minute. This produced a heat pulse of 120 joules. The rubber bands that I used were natural rubber, 3-1/2 inch circumference by 1/2 inch width, with a 2.5 gram weight (Staples #84). To maximize response, one band was placed inside another to give a combined weight of 5 grams. The data for one experiment in which a doubled band was twisted and untwisted 50 turns is shown below.

Elastocaloric experimental data

Elastocaloric effect experimental data. Even the best calorimeters give data on a drifting baseline, and the usual method for extracting the data is shown. It's easily seen that twisting and untwisting do not produce the same heat, a consequence of the heat produced by friction, as explained in the text. (Graphed using Gnumeric. Click for larger image.)


According to the elastocaloric effect, heat is released when a rubber band is stretched, and then absorbed when the stretch is relaxed. It can be seen from the above data that the measured heats are different. The problem is the friction produced when the rubber strips rub against each other. As can be seen in the photograph, there's a lot of rubbing.

Rubber band twisted 40 turns

Rubber bands twisted 40 turns in the calorimeter. These bands break at about 60 turns, so 50 turns were used to give maximal effect.


This rubbing is the same during twisting and untwisting, and this allows elimination of the frictional heat F in a calculation of the elastocaloric heat H.
Twisting: H + F = 105 j

Untwisting: H - F = 41 j

H = 73 j

H = 14.6 j/g
This elastocaloric specific heat, 14.6 j/g, is close to that reported in similar experiments.[4-5] As you can see, this effect is very small.

References:

  1. Ashutosh Jogalekar, "Ernest Rutherford, master of simplicity," Scientific American Blogs, August 30, 2013.
  2. Facts and Figures about the LHC, CERN Website.
  3. D.M. Gualtieri and P.J. Ficalora, Electron Transfer and Metallic Bonding: The Heats of Reaction of FeAl3-x(Ag;Zn;Pt;Au)x Alloys, High Temperature Science 7, 25-36 (1975).
  4. Run Wang, Shaoli Fang, Yicheng Xiao, Enlai Gao, Nan Jiang, Yaowang Li, Linlin Mou, Yanan Shen, Wubin Zhao, Sitong Li, Alexandre F. Fonseca, Douglas S. Galvão, Mengmeng Chen, Wenqian He, Kaiqing Yu, Hongbing Lu, Xuemin Wang, Dong Qian, Ali E. Aliev, Na Li, Carter S. Haines, Zhongsheng Liu, Jiuke Mu, Zhong Wang, Shougen Yin, Márcio D. Lima, Baigang An, Xiang Zhou, Zunfeng Liu, and Ray H. Baughman, "Torsional refrigeration by twisted, coiled, and supercoiled fibers," Science, vol. 366, no. 6462 (October 11, 2019), pp. 216-221, DOI: 10.1126/science.aax6182.
  5. George Musser, "A fridge made from a rubber band? Twisted elastic fibers could cool your food," Science, October 10, 2019, doi:10.1126/science.aaz8133.

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