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== Abstract ==

== Abstract ==

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. The average energy per particle for an ensemble in equilibrium is called temperature, according to the kinetic theory.  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).  

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. Each particle can have a random amount of energy from the pool, but one particle that uses a lot of energy, would leave less energy for the rest of the particles. Therefore, the energy distribution in thermal equilibrium at temperature T is an exponential distribution. This means that 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 experiment has been carried out using a novel detector comprised of a large array of silicon avalanche photodiodes known as a silicon photomultiplier (SiPM). It stores a large amount of energy and releases it if there is a slight disturbance. From time to time, an electron would have enough energy to set off the silicon photomultiplier from the randomness of the thermal energy distribution. This mechanism reacts to the energy of a single electron, allowing us to detect the thermal energies of a single particle.  

 

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.

[[Counting individual photons|Back]]

[[Counting individual photons|Back]]