Radioactive Heat

July 26, 2011

Radionuclides emit heat even when they're not lumped into huge piles, as in a nuclear fission reactor. Reasonably small quantities of radioactive material are used in devices called radioisotope thermoelectric generators that convert the emitted heat to useful electrical power. This is usually done using the Seebeck effect in which an array of thermocouples is employed with their hot junctions at the radioisotope, and their cold junctions at a suitable low temperature sink.

As can be imagined, the efficiency of such devices depends as much on the availability of cold as they do on the heat of the radioisotope. This is yet another example of the second law of thermodynamics at work (For and exposition of the second law, see my previous article, Second Law of Thermodynamics, February 7, 2011). This makes such generators ideal in a space environment where the cold of deep space works to their favor.

NASA has developed a number of radioisotope thermoelectric generators, one of the more powerful being the General Purpose Heat Source Radioisotope Thermoelectric Generator, used most famously on the Cassini-Huygens spacecraft to Saturn. This generator contains 7.8 kg of plutonium-238 (²³⁸Pu) as the heat source. This generator produced 300 watts of electrical power while the spacecraft was in Earth's vicinity. Since the efficiency of thermoelectric conversion is so low, 4,400 watts of thermal energy are required to produce these 300 electrical watts.

Also capitalizing on the availability of a cold sink, the Soviet Union deployed such units for lighthouse power in the Arctic Ocean. However, the problems of having such a compact source of radioactive material available to terrorists have discouraged such terrestrial usage. Even after the devices have outlived their usefulness as a power source, when the material has too far decayed, the remaining material still poses a great hazard.

The Earth, itself, contains huge quantities of radioactive elements in its mantle and crust. It's aways been thought that decay of these radionuclides helped to keep the Earth warm. However, the exact percentage of heat that radioactive decay supplies compared with the residual heat of Earth's formation was not really known. A recent paper posted on the Nature Geoscience website, and soon to be published in the journal, provides evidence that the decay of potassium, uranium and thorium provides about half of Earth's internal heat.[1-3]

Sitting on a furnace. The heat flux from the Earth into space is about 44 trillion watts. (Lawrence Berkeley National Laboratory Image).

To say that this research was performed by an international collaboration is somewhat of an understatement. This work was performed by the "KamLAND Collaboration," which includes scientists from fifteen organizations in Japan, the United States and The Netherlands. By my count, there are eighty scientists who contributed to this project. KamLAND stands for Kamioka Liquid-scintillator Antineutrino Detector.

KamLAND was designed for another purpose; namely, detection of antineutrinos from nuclear reactors in Japan in order to study neutrino oscillation. Electron neutrinos are produced in nuclear reactors, but they oscillate into the two other neutrino "flavors," muon and tau as they travel.[2] This same detector will detect geoneutrinos, neutrinos released during the decay of radioactive elements in the Earth, and thus measure the decay rates and types. The neutrino detector inside Japan's Mount Ikenoyama collected data from March 2002 through November 2009.[3] This study also used data from the Borexino detector in Italy.

The KamLAND detector, as shown in the figure, is a sphere containing a thousand metric tons of scintillating mineral oil surrounded by more than 1,800 photomultiplier tubes. It's located underground near Toyama, Japan.[2] Detection is aided by a double-scintillation that occurs when an antineutrino interacts with a proton in the fluid. This reaction converts the proton to a neutron and a positron. The positron is then annihilated by an electron, causing an initial scintillation. A few microseconds later, the neutron binds with a proton to emit a gamma ray with emission of a second scintillation. Careful analysis of the scintillations allows discrimination of such signals from a cosmic ray background.[2]

The KamLAND antineutrino detector is a spherical vessel, filled with scintillating mineral oil, and lined with photomultiplier tubes. It's located underground, near Toyama, Japan. The scale can be seen from the seated technicians pictured in the control room. (KamLAND Collaboration Image, via Lawrence Berkeley National Laboratory).

The data show that uranium-238 and thorium-232 together account for about 20 terawatts of Earth's heat flux. Potassium-40 is a big contributor, but it was below the detection limit. Potassium-40 is estimated to contribute about four terrawatts. These three elements generate about half Earth's heat flux in toto.[1] Because of the inevitable radioactive decay process, the Earth is currently cooling at a rate of approximately 100 degrees Celsius each 1 billion years.[3]

Statistics are hard for neutrinos. Of those detected, 485 were produced from manmade sources, such as nuclear reactors and nuclear waste. Another 245 were likely produced by cosmic ray interaction with Earth's atmosphere. Just 111 neutrinos could be associated with Earth's natural radioactivity, of which only 106 were definite candidates.[3]

The team estimates that the overall neutrino flux from uranium-238 and thorium-232 decay at Earth's surface is 4.3 million per square centimeter per second.[3] It's a good thing that neutrinos don't interact much with matter (they interact only via the weak force and gravity), or we wouldn't be here! This flux points to a 54% contribution of radioactive decay to Earth's heat, with eight terawatts from uranium-238 (²³⁸U), eight terawatts from thorium-232 (²³²Th), and four terawatts from potassium-40 (⁴⁰K).[2]

References:

1. The KamLAND Collaboration, "Partial radiogenic heat model for Earth revealed by geoneutrino measurements," Nature Geoscience, Published online 17 July 2011; Supplementary Information.
2. Paul Preuss, "What Keeps the Earth Cooking? Berkeley Lab scientists join their KamLAND colleagues to measure the radioactive sources of Earth’s heat flow," Lawrence Berkeley Laboratory Press Release, July 17, 2011
3. Half Of Earth's Internal Heat Comes From Radioactive Decay, RedOrbit, July 18, 2011.