Engineering Questions with Answers - Multiple Choice Questions

# Aerodynamics – Vibrational Rate Equations

1 - Question

What is the value of transition probability?
a) 0
b) More than 1
c) Less than 1
d) 1
Explanation: Transition probability is the probability that a molecule will jump to another i + 1 level after the molecular collision. The transition of the molecule moving to a higher energy level requires several number of collisions. This probability value is always less than 1.

2 - Question

What does the product of collision frequency and transition probability yield?
a) Number of transitions per particle per second
b) Number of collisions per second
c) Number of collisions per second per particle
d) Transitions per collision
Explanation: The collision frequency (Z) when multiplied with the transition probability (Pi, i + 1) yield the number of transitions per particle per second. Since the collision frequency is the number of collisions taking place per particle and the transition probability gives the number of transitions taking place per collision per particle.

3 - Question

What is the formula to compute net rate change of the population of the ith level?
a) dNidt = Pi + 1, i ZNi + 1 + Pi – 1, i ZNi – 1 – Pi, i + 1 ZNi – Pi, i – 1 ZNi
b) dNidt = – Pi + 1, i ZNi + 1 + Pi – 1, i ZNi – 1 + Pi, i + 1 ZNi + Pi, i – 1 ZNi
c) dNidt = Pi + 1, i ZNi + 1 – Pi, i + 1 ZNi
d) dNidt = + Pi – 1, i ZNi – 1 – Pi, i – 1 ZNi
Explanation: The rate of change of population of the molecules in ith level is computed by adding rate of increase of Ni (population of ith level) and rate of decrease of Ni. Thus the formula is: dNidt = Pi + 1, i ZNi + 1 + Pi – 1, i ZNi – 1 – Pi, i + 1 ZNi – Pi, i – 1 ZNi Where, Pi + 1, i ZNi + 1 + Pi – 1, i ZNi – 1 is the rate of increase of population in ith level due to the molecules jumping up from i – 1 and down from i + 1 levels. Pi, i + 1 ZNi – Pi, i – 1 ZNi is the rate of decrease of population in the ith level due to the molecules jumping from ith level to i + 1 and i – 1 levels.

4 - Question

What is the master equation for vibrational relaxation?
a) dNidt = ki + 1, i ZNi + 1 + ki – 1, i ZNi – 1 – ki, i + 1 ZNi – ki, i – 1 ZNi
b) dNidt = ki + 1, i Ni + 1 + ki – 1, i Ni – 1 – ki, i + 1Ni – ki, i – 1 Ni
c) dNidt = ZNi + 1 + ZNi – 1 – ZNi, i – 1 – ZNi
d) dNidt = Pi + 1, i ZNi + 1 + Pi – 1, i ZNi – 1
Explanation: In the formula derived to obtain then net rate of change of population of the ith 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 dNidt = Pi + 1, i ZNi + 1 + Pi – 1, i ZNi – 1 – Pi, i + 1 ZNi – Pi, i – 1 ZNi to: dNidt = ki + 1, i Ni + 1 + ki – 1, i Ni – 1 – ki, i + 1Ni – ki, i – 1 Ni

5 - Question

Which of these is the vibrational rate equation?
a) devibdt=1τ(eeqvib – evib)
b) τ = 1k1,0(1–e−hv/kT)
c) evib = τ(eeqvib – evib)
d) devibdt = 1τ(eeqvib – evib)