Adiabatic and isothermal changes
When a gas is compressed or
expanded there are many possible connections between the changes of pressure, volume
and temperature. We will restrict ourselves to looking at just two basic
variations.
(i) Isothermal expansion or compression
In an
isothermal change the temperature of the gas is kept constant during
the change in pressure and volume by adding or removing heat energy from the system. For
this reason isothermal changes should take place in thin-walled, conducting
containers.
For this type of change T= constant and therefore PV = constant; the
gas obeys Boyle's law (Figure 1).
(ii) Adiabatic expansion or
compression
In an
adiabatic change the total heat
content of the system is kept constant and therefore the temperature of the gas will alter; no
heat must enter or leave the system. This type of change should occur in an insulated
container.
Since the temperature of the gas changes the adiabatic curves for PV will
be steeper than those for an isothermal change (Figure 2). True adiabatic changes are
difficult to produce in reality, but the expansion of air from a burst tyre or balloon and the
expansion and compression of air through which a sound wave is passing are very close to
adiabatic changes.
Isothermal graphs at
different temperatures
The following graphs show the PV curves for isothermal
changes for a given mass at two different temperatures T
o and T
1
where T
1>T
o.
Temperature variation in a reversible
adiabatic change
When a gas in an insulated container is compressed or
expanded it suffers a change in temperature, the molecules of gas gaining energy from, or
losing energy to, the moving walls of the container.
Consider a volume of gas enclosed in an
insulating container by a frictionless piston. Let the initial velocity of a molecule moving in the
x-direction be u.
(a) If it collides with a stationary wall of the container its velocity after
collision will be -u (see Figure 4 (a)).
Now consider the case when the wall is
moving at velocity v, first an expansion and then a compression (Figures 4(b) and
(c)).
(b) The velocity of the molecule relative to the wall = u - v.
After
collision:
velocity relative to the wall = - (u - v) velocity relative to the Earth = -
(u - 2v)
The final velocity is less than the initial velocity by 2v, and so the gas has cooled.
Notice that this cooling only takes place while the wall of the container is moving.
(c)
Similarly for the compression we can say that, after collision, the velocity relative to the Earth
= - (u + 2v)
This shows an increase in velocity, and therefore the temperature of the gas
will be raised
