InterviewSolution
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InterviewSolution
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What is the master equation for vibrational relaxation?(a) \(\frac {dN_i}{dt}\) = ki + 1, i ZNi + 1 + ki – 1, i ZNi – 1 – ki, i + 1 ZNi – ki, i – 1 ZNi(b) \(\frac {dN_i}{dt}\) = ki + 1, i Ni + 1 + ki – 1, i Ni – 1 – ki, i + 1Ni – ki, i – 1 Ni(c) \(\frac {dN_i}{dt}\) = ZNi + 1 + ZNi – 1 – ZNi, i – 1 – ZNi(d) \(\frac {dN_i}{dt}\) = Pi + 1, i ZNi + 1 + Pi – 1, i ZNi – 1This question was addressed to me in an international level competition.My doubt stems from Vibrational Rate Equations in division Properties of High Temperature Gases of Aerodynamics |
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Answer» CORRECT choice is (b) \(\frac {dN_i}{DT}\) = ki + 1, i Ni + 1 + ki – 1, i Ni – 1 – ki, i + 1Ni – ki, i – 1 Ni To explain: In the formula derived to obtain then net rate of change of population of the i^th level, the product of TRANSITION probability and collision frequency is expressed in the form of a new variable known as vibrational rate constant ki + 1, i = PI + 1, i Z (this is an example of ONE of the transitions). Thus the formula is reduced from \(\frac {dN_i}{dt}\) = Pi + 1, i ZNi + 1 + Pi – 1, i ZNi – 1 – Pi, i + 1 ZNi – Pi, i – 1 ZNi to: \(\frac {dN_i}{dt}\) = ki + 1, i Ni + 1 + ki – 1, i Ni – 1 – ki, i + 1Ni – ki, i – 1 Ni |
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