The macroscopic properties of a gas, pressure and temperature, are explained in terms of molecule movement of the Kinetic Theory. The derivation of formulas are shown in logical steps for pressure, temperature and KE.

1. Pressure, Temperature and
‘RMS’ related to kinetic model
Lesson Opener: How does Pressure of a Gas
relate to the motion of particles in the Molecular
Kinetic Theory?
NIS, Taldykorgan
Grade 11 Physics

2. Objective 1:
• Explain how molecular movement causes the
pressure exerted by a gas and hence deduce
the relationship:
– Kazakh /Russian
p=pressure
n=molecular density
m0=mass of a molecule
<v>2= average velocity
IB, SAT and Giancoli
P=pressure
N=Number of molecules
m=mass of a molecule
V=volume
=average velocity

3. WHAT CAUSES PRESSURE in a GAS?
IF MOLECULES MOVE
FASTER AND COLLIDE
MORE OFTEN, THEY HAVE
MORE FORCE.
PRESSURE INCREASES!
When you shack a bottle of
soda, the gas molecules move
faster, pressure increases, when
opened the higher pressure
‘explodes’ with the soda making a
big mess.

4. How Does KT explain Pressure?
Elastic collisions causes a force
on the sides of the container.
The force depends on:
•Mass of molecules
•Velocity of molecules
•Number of molecules
N=Number of molecules
m=mass of a molecule
=average velocity

5. Deduce (or Derive) this relationship…
One molecule creates a force by
its change in momentum
F= Change in momentum
change in time
F = Δmvx = mvx-(-mvx) =2mvx
Δt
Δt
2L/vx
F = mvx2 P = F = mvx2 /L
L
A
L2
P= mvx2 = mvx2 This Pressure for
L3
V
for one molecule
2L= vxΔt → Δt = 2L/vx

6. The Pressure for N molecules and
‘mean square velocity’
• N molecules move at an
average velocity = N
• Velocity is a vector so
In Russian/Kazakh
‘n’ = N/V and is called
molecular density.
So the Course Plan
Formula is
and
• So P = 1 Nm
3V
‘n’ = N
V
(only here does ‘n’=
molecular density)

7. YouTube Presentation of Pressure
• Derivation of Pressure Formula:
http://www.youtube.com/watch?v=CmerWVk
0ZaI

8. Root Mean Square Speed
• Objective 2: Recall and understand the term
root mean-square velocity (average = mean)
• Simply – ‘the square root of the average velocity’
• Why? Velocities are + and - , so an average would
be zero!
• Squaring first gives all positive velocities
• Taking the square give the average speed without
direction.
Also used in AC current
calculations in year 12!

9. Why and Where do we need RMS?
To find the velocity of molecules at T!
• Start with
→
• Remember: PV = NkT
• Therefore:
→
• Now, to find velocity we need to take the
square root of the ‘average square velocity’!

10. Uses of RMS Velocity
• RMS speed is used to predict how fast molecules
are moving at a given Temperature.
How fast molecules move
is directly proportional to
their absolute temperature
and inversely proportional
to their mass.
vrms
3RT
M
Because:

11. Example: Determine the Speed of Molecules in Air at 293 K?
N2 molecules (molecular mass 28.0 u)
3RT
O2 molecules (molecular mass 32.0 u)
vrms
M
For nitrogen…
3RT
vrms
M
3 8.31J mol K 293 K
0.0280 kg mol
511 m s
3 8.31J mol K 293 K
0.0320 kg mol
478 m s
For oxygen…
vrms
3RT
M

12. At the same temperature…
• Small molecules move fast
• Large molecules move slow

13. Important features of Maxwell-Boltzmann distribution :
The speed-density relationship of 4 Gases at 298.15 K (25 °C).

14. Kinetic Energy and Temperature:
• Objective 3: “compare
and PV=NkT
and hence deduce that the average kinetic energy of a
molecule is proportional to T” !
• Remember that
• Therefore
and

15. References:
• Learn Physics: Learn about Kinetic Theory of
Gases (good animation)
http://www.youtube.com/watch?v=YSTRa27a3BQ
• Pressure and RMS Velocity (Easy Formulas)
http://www.youtube.com/watch?v=CmerWVk0ZaI