Pressure can be calculated using several different units. The force on
an object is given by the product of the mass, m, and the acceleration, a,
according to Newton’s law:
F=ma (1.2)
Remember that the rate of change in position gives the velocity, 9 , and
acceleration is the rate of change of velocity:
(1.3)
Acceleration has units of distance time−^2 or m s−^2 , so force has units of
kg(m s−^2 ). Dividing the force by area gives the standard unit for pressure
called the Pascal, Pa:
(1.4)
Since thermodynamics is intimately related to energy, it is convenient to
consider in terms of energy. Energy, E, is given by the product of the force
exerted over a distance:
E=F ×d (1.5)
The unit of energy is Joules, J, that can be written as:
(1.6)
Comparing the units for pressure (eqn 1.4) and energy (eqn 1.5) allows the
units for pressure to be rewritten as:
(1.7)
Pressure can be expressed in terms of an energy per volume. A variety
of units are used to describe pressure. One convenient unit is to express
the pressure in terms of the pressure that our atmosphere exerts at sea
level, or 1 atm. The units for Pascals and atmospheric pressure can be
converted using:
1 atm =101,325 Pa (1.8)
Pa
J
m= 3
Jkg
m
smkg m
s= ()
⎛
⎝
⎜⎜
⎞
⎠
2 ⎟⎟ =
2
2Pa kg
m
sm
kg
ms=
⎡
⎣
⎢
⎢
⎤
⎦
⎥
⎥
⎡
⎣
⎢
⎢
⎤
⎦
⎥
⎥
22 = − 2
1
a
tt
x
t==
⎛
⎝
⎜⎜
⎞
⎠
⎟⎟
d
dd
dd
d9
9 =
d
dx
t