Page 123 - Physical chemistry understanding our chemical world

90 ENERGY AND THE FIRST LAW OF THERMODYNAMICS

Alternatively, we could consider inflating the tyre with a series of, say, 100 short
steps – each separated by a short pause. The difference in pressure before and after
each of these small steps would be so slight that the gas within the tyre would be
allowed to reach equilibrium with its surroundings after adding each increment, and
before the next. Stated a different way, the difference between the pressure of the gas
in the hand pump and in the tyre will always be slight.
We can take this idea further. We need to realize that if there is
‘Infinitesimal’ is the no real difference in pressure between the hand pump and the gas
reciprocal of infinite, within the tyre, then no work would be needed to inflate because
i.e. incredibly small. there would never be the need to pump against a pressure. Alter-
natively, if the inflation were accomplished at a rate so slow that it
was infinitesimally slow, then there would never be a difference in pressure, ensuring
w was always zero. And if w was zero, then U would stay constant per increment. (We
need to be aware that this argument requires us to perform the process isothermally.)
It should be clear that inflating a tyre under such conditions is never going to occur
in practice, because we would not have the time, and the inflation would never be
complete. But as a conceptual experiment, we see that working at an infinitesimally
slow rate does not constitute work in the thermodynamic sense.
It is often useful to perform thought experiments of this type,
A thermodynamic pro- changing a thermodynamic variable at an infinitely slow rate: we
cess is reversible if an say we perform the change reversibly. (If we perform a process in a
infinitesimal change in non-reversible manner then we say it is ‘irreversible’.) As a simple
an external variable definition, a process is said to be reversible if the change occurs
(e.g. pressure) can at an infinitesimal rate, and if an infinitesimal change in an exter-
change the direction nal variable (such as pressure) could change the direction of the
in which the process thermodynamic process. It is seen that a change is only reversible
occurs.
if it occurs with the system and surroundings in equilibrium at
all times. In practice this condition is never attained, but we can
sometimes come quite close.
The amount of work Reversibility can be a fairly difficult concept to grasp, but it
that can be performed is invaluable. In fact, the amount of work that can be performed
during a thermody- during a thermodynamic process is maximized when performing
namic process is maxi- it reversibly.
mized by performing it The discussion here has focused on work done by changes in
reversibly. pressure, but we could equally have discussed it in terms of volume
changes, electrical work (see Chapter 7) or chemical changes (see
Chapter 4).

How fast does the air in an oven warm up?

Absorbing energy

The air inside an oven begins to get warm as soon as we switch it on. We can
regard the interior of the oven as a fixed system, so the internal energy U of the