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Line 1: − Temperature is a factor in every part of our lives; everything that we do is affected by it. All the effects of temperature that we experience are due to the cumulative effects of the energies of trillions of particles. The temperatures that we experience everyday are due to the consequence of the average thermal energies of millions and billions of particles working together. + − The thermal energy of a single particle is very different from average energies. Statistical physics predicts the probability variation of temperature to be an exponential curve; with many particles with small energies and very few particles with large amounts of energy. This information can be used to measure single particles. It is easier to measure the particles with the more energy. This experiment uses a Silicon Photomultiplier (SiPM) to detect the thermal energy of the particles with the most energy. − An SiPM uses the technology previously employed in the Avalanche Photodiode. A diode is reverse-biased until just before breakdown voltage and it stays at that state until a source of energy (such as thermal energy) pushes it past breakdown. It then releases all of its charge and then slowly resets. An SiPM is different in that it uses an array of many Avalanche Photodiodes are made into a silicon wafer. The photodiodes are so small that they can be counted as individual pixels. Therefore, an SiPM can determine how many particles have enough energy to set it off. Every time a photodiode fires, a current runs though the SiPM. By measuring the energy released by the SiPM, the number of individual particles which have enough energy to set off the SiPM can be determined. − (Calibration should be in the Methods and Materials?) − An SiPM was calibrated using electromagnetic energy instead of thermal energy because electromagnetic energy is easier to control. A dark box was set up with a LED at one end and the SiPM in another. Since each photon that hit the SiPM reliably produced an effective pulse, it was possible to calculate the number of pixels fired. This made it possible to calculate the amount of energy released if a single pixel was fired. +
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The kinetic theory explains temperature as the collective effect of the motion of many particles. Usually these collective effects are only observed as the average behavior of millions of billions of particles, which all share a common pool of energy. According to kinetic theory, all of the particles which share a common pool of energy are called members of an ensemble. Each member is free to use a random amount of energy from the shared pool, but one particle using a lot of energy leaves less energy for the other particles. This means that the majority of the particles in an ensemble have energies close to or less than the average energy, while a few of them have energies much larger than the average. When the energy distribution of the ensemble reaches a steady state, the ensemble is said to be in thermal equilibrium. According to this kinetic theory, the average energy per particle for an ensemble in equilibrium is called temperature. The energy distribution of the members of an ensemble in thermal equilibrium at temperature T is an exponential distribution with an average energy kT, where k (Boltzmann's constant) is there in order to convert temperature from degrees Kelvin to units of energy (Joules).
According to the exponential distribution, very few particles have a large amount of kinetic energy, but no matter how high the energy or how low the temperature, the population is never quite zero. This means that even processes that require very large amounts of energy will take place in a system in thermal equilibrium at any temperature, given enough time. An interesting test of this theory would be to set up an experiment to look for those rare instances when an ensemble contains a particle with energy many times the average given by the temperature. This experiment has been carried out using a novel detector comprised of a large array of silicon avalanche photodiodes known as a silicon photomultiplier (SiPM). The avalanche photodiode works like a mousetrap, storing a large amount of energy and then releasing it suddenly in response to a weak disturbance. In its intended mode of operation, the weak disturbance is provided by the absorption of a single photon of visible light in the region of the diode junction. In this experiment, the device was shielded from all external light sources, so that the only possible trigger mechanism is the internal motion of electrons within the junction itself. According to the kinetic theory, even without photons to excite the electrons over the trigger threshold, from time to time an electron should acquire enough energy to simulate an absorbing photon just from the randomness of the thermal energy distribution. The rate at which these thermal triggers occur is predicted by the kinetic theory, based on the exponential distribution, the temperature of the junction, and the number of electrons in the region of the junction. This mechanism reacts to the energy of a single electron, allowing us to detect the thermal energies of a single particle.
[[Counting individual photons|Back]]
[[Counting individual photons|Back]]