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INTRODUCTION TO THERMODYNAMICS: INTERNAL ENERGY 89

energy is negative. If U is negative and q = 0, then w is also negative. By corollary,
the value of w in Equation (3.5) is negative whenever the gas performs work.
From Chapter 2, we remember again that the simplest way to tell whether the
internal energy decreases is to check whether the temperature also decreases. We see
that the gas coming from the tyre is cold because it performs work, which decreases
its internal energy.

Why does a tyre get hot during inflation?
Adiabatic changes

Anyone inflating a tyre with a hand pump will agree that much
The temperature of
hard work is needed. A car or bicycle tyre usually gets hot during
atyrealsoincreases
inflation. In the previous example, the released gas did thermody-
when inflated, and is
namic work and the value of w was negative. In this example, work caused by interparticle
is done to the gas in the tyre, so the value of w is positive. Again, interactions forming;
we assume that no energy is transferred, which again allows us to see p. 59.
take q as zero.
Looking again at Equation (3.5), U = q + w, we see that if
q = 0 and w increases (w is positive), then U increases. This increase in U
explains why the temperature of the gas in the tyre increases.
Let us return to the assertion that q is zero, which implies that the system is ener-
getically closed, i.e. that no energy can enter or leave the tyre. This statement is
not wholly true because the temperature of the gas within the tyre will equilibrate
eventually with the rubber of the tyre, and hence with the outside air, so the tyre
becomes cooler in accordance with the minus-oneth and zeroth laws of thermody-
namics. But the rubber with which tyre is made is a fairly good thermal insulator,
and equilibration is slow. We then make the good approximation that the system is
closed, energetically. We say the change in energy is adiabatic.
Energetic changes are adiabatic if they can be envisaged to occur
while contained within a boundary across which no energy can A thermodynamic pro-
pass. In other words, the energy content within the system stays cess is adiabatic if
fixed. For this reason, there may be a steep temperature jump in it occurs within a
going from inside the sealed system to its surroundings – the gas (conceptual) bound-
in the tyre is hot, but the surrounding air is cooler. ary across which no
In fact, a truly adiabatic system cannot be attained, since even energy can flow.
the most insulatory materials will slowly conduct heat. The best
approximations are devices such as a Dewar flask (sometimes called a ‘vacuum
flask’).

Can a tyre be inflated without a rise in temperature?
Thermodynamic reversibility

A tyre can indeed be inflated without a rise in temperature, most simply by filling
it with a pre-cooled gas, although some might regard this ‘adaptation’ as cheating!