Dimensional Analysis
In class you were asked to prove that Pascal X meter3 = Joules. It was demonstrated that a Pascal =
Newton/m2 (which was a hint on how to approach this).
From Physics you should recall
Pressure = Force/Area,
Force = Mass x Acceleration,
Using the MKS or (SI) units
Force
Newton =
kg-m
sec 2
E = mc2 (or any definition of energy)
acceleration is meters/sec2 and mass is the kilogram.
= mass x acceleration
Newton = kg x
and
meter
second 2
force
area
Newton
=
meter 2
kg-m/sec 2
kg
=
=
2
m
m-sec 2
Pressure
=
Pascal
Pascal
Recalling Einstein’s equation E = m c2  Since energy is measured in Joules, m stands for mass (kg)
and c is the speed of light (m/sec), then a Joule must be the same thing as kg-m2/sec2.
Finally:
! Newton $
Pressure times volume = Pascals x meters 3 = #
meters 3 = Newton-meters
" meter 2 &%
(
)
! kg-m $
N-m = #
( m ) = kg-m 2 /sec 2 which is the same things as a Joule
" sec 2 &%
Thus it has been shown that Pa x m3 is the same thing as a Joule
Lastly:
Since 1000 Liters = 1 m3 and 1 kiloPascal = 1000 Pascal
" 1
%
Pascal ! meter 3 = $
kPa ' ! (1000 L ) = KiloPascal ! Liter = Joules
# 1000
&
For example:
R = 8.31447 Pascals-meters 3 /mole-Kelvin = 8.31447 kPa-L/mol-K = 8.31447 Joule/mol-K
All of this should have been covered in General Chemistry I and/or University (or College) Physics I.
You are expected to know ALL of this