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| {{for|a discussion about the meaning of the term in classical thermodynamics|Exergy}}
| | Friends call him Royal. Managing people is how I make money and it's something I truly appreciate. To keep birds is one of the things he enjoys most. Her family lives in Idaho.<br><br>Feel free to surf to my blog post; car warranty, [http://112.217.168.194/onsesang/xe/index.php?document_srl=10158&mid=comm_info01 describes it], |
| {{Unreferenced|date=February 2007}}
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| In [[particle physics]], the '''available energy''' is the energy in a particle collision available to produce new matter from the [[kinetic energy]] of the colliding particles. Since the conservation of [[momentum]] must be held, a system of two particles with a net momentum may not convert all their kinetic energy into [[mass]] - and thus the available energy is always less than or equal to the kinetic energy of the colliding particles. The available energy for a system of one stationary particle and one moving particle is defined as:
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| :<math> E_a = \sqrt{2 E_t E_k + (m_t c^2)^2 + (m_k c^2)^2} </math>
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| where
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| : <math> E_t </math> is the total energy of the target particle,
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| : <math> E_k </math> is the total energy of the moving particle, | |
| : <math> m_t </math> is the mass of the stationary target particle,
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| : <math> m_k </math> is the mass of the moving particle, and
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| : <math> c </math> is the [[speed of light]].
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| ==Derivation==
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| Suppose the following:
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| :<math> E_a = E_k + E_t </math>
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| We know that since
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| :<math> E = m c^2 </math>
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| must hold, then
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| :<math> E_k = m_k c^2 </math>
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| and
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| :<math> E_t = m_t c^2 </math>
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| should both hold. From here, we can see that
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| :<math> E_a = m_k c^2 + m_t c^2 </math>
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| Squaring both sides, we get
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| :<math> (E_a)^2 = (m_k c^2 + m_t c^2)^2 </math>
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| Expanding, we can see that
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| :<math> (E_a)^2 = ((m_k c^2)^2 + (m_t c^2)^2 + 2 (m_t c^2) (m_k c^2)) </math>
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| Taking the square root of both sides,
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| :<math> E_a = \sqrt{(m_k c^2)^2 + (m_t c^2)^2 + 2 (m_t c^2) (m_k c^2)} </math>
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| Evaluating the inside of the square root, we see that
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| :<math> E_a = \sqrt{(m_k c^2)^2 + (m_t c^2)^2 + 2 E_k E_t} </math>
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| Which can be rearranged to form the original equation,
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| :<math> E_a = \sqrt{2 E_t E_k + (m_t c^2)^2 + (m_k c^2)^2} </math>
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| ==See also==
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| *[[Threshold energy]]
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| *[[Matter creation]]
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| ==References==
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| {{reflist}}
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| ==External links==
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| [[Category:Particle physics]]
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| {{physics-stub}}
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Friends call him Royal. Managing people is how I make money and it's something I truly appreciate. To keep birds is one of the things he enjoys most. Her family lives in Idaho.
Feel free to surf to my blog post; car warranty, describes it,