School of Aerospace Engineering
Gas Kinetic Theory
Introduction to Chem. Thermo/Kinetics -1
Copyright © 2003 by Jerry M. Seitzman and Jeff Jagoda. All
rights reserved.
Chemical Thermo. and Gas Kinetics
School of Aerospace Engineering
Molecular Model
• Molecules consist of one or more atoms
each of which is made up of a nucleus
surrounded by electrons.
• One kg.mole consists of 6x1026 molecules
(Avogadro’s Number).
• A perfect gas at STP contains 3x1025
molecules/m3
Introduction to Chem. Thermo/Kinetics -2
Copyright © 2003 by Jerry M. Seitzman and Jeff Jagoda. All
rights reserved.
Chemical Thermo. and Gas Kinetics
School of Aerospace Engineering
Molecular Model
• Molecules move at near the speed of
sound.
• Molecules move in straight lines unless
they interact with a wall or each other.
• Molecules react with each other; they
attract each other over “longer” distances
(few molecular radii); repel each other
when closer.
Introduction to Chem. Thermo/Kinetics -3
Copyright © 2003 by Jerry M. Seitzman and Jeff Jagoda. All
rights reserved.
Chemical Thermo. and Gas Kinetics
School of Aerospace Engineering
Molecular Model
Introduction to Chem. Thermo/Kinetics -4
Copyright © 2003 by Jerry M. Seitzman and Jeff Jagoda. All
rights reserved.
(add PE graph)
Chemical Thermo. and Gas Kinetics
School of Aerospace Engineering
Simplified Molecular Model
• Molecules behave like billiard balls.
• Molecules interact with each other and with walls
by perfectly elastic collisions.
• Molecules distributed uniformly in volume under
consideration.
• Molecular motion in all directions equally likely.
Introduction to Chem. Thermo/Kinetics -5
Copyright © 2003 by Jerry M. Seitzman and Jeff Jagoda. All
rights reserved.
Chemical Thermo. and Gas Kinetics
School of Aerospace Engineering
Vector/Velocity Space
• Attach velocity vector to each of the N
molecules and place at origin.
• Draw sphere radius r, centered about
origin
• Extend vectors to intersect sphere.
• For random motion: N/4pr2 intersections
per unit area
Introduction to Chem. Thermo/Kinetics -6
Copyright © 2003 by Jerry M. Seitzman and Jeff Jagoda. All
rights reserved.
Chemical Thermo. and Gas Kinetics
School of Aerospace Engineering
Vector/Velocity Space
Introduction to Chem. Thermo/Kinetics -7
Copyright © 2003 by Jerry M. Seitzman and Jeff Jagoda. All
rights reserved.
Chemical Thermo. and Gas Kinetics
School of Aerospace Engineering
Vector/Velocity Space
Consider a small area increment on the
sphere: dA = (r dq)(r sinqdf)
Then # of molecules moving in the direction
between q, q+dq and f, f+df is given by:
d2Nq,f= (N/4pr2).dA =
(N/4p)(sin qdq df)
(1)
The # of such molecules/unit volume:
d2nq,f= (n/4p)(sin qdq df)
(2)
Introduction to Chem. Thermo/Kinetics -8
Copyright © 2003 by Jerry M. Seitzman and Jeff Jagoda. All
rights reserved.
Chemical Thermo. and Gas Kinetics
School of Aerospace Engineering
Vector/Velocity Space
• Molecules have a distribution of speeds
(see later).
• Let dNv be the number of molecules
moving with a speed between v, v+dv.
• Then dNv or dnv is represented by a
spherical shell thickness dv.
• In equilibrium molecules change velocity
all the time but dNv remains constant.
Introduction to Chem. Thermo/Kinetics -9
Copyright © 2003 by Jerry M. Seitzman and Jeff Jagoda. All
rights reserved.
Chemical Thermo. and Gas Kinetics
School of Aerospace Engineering
Vector/Velocity Space
Introduction to Chem. Thermo/Kinetics -10
Copyright © 2003 by Jerry M. Seitzman and Jeff Jagoda. All
rights reserved.
Chemical Thermo. and Gas Kinetics