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88 ENERGY AND THE FIRST LAW OF THERMODYNAMICS

The definition of U is given by Equation (3.1):

U = U (final) − U (initial)
Rearranging to make U (final) the subject, we obtain
Care:thisisa highly
artificial calculation and
is intended for illus- U (final) = U (initial) + U
trative purposes only.
In practice, we never Equation (3.5) is another expression for U. Substituting for U in
know values of U,only Equation (3.1) allows us to say
changes in U,i.e. U.
U (final) = U (initial) + q + w
Inserting values into this equation, we obtain

The word ‘isothermal’
can be understood by U (final) = 4000 J + 20 000 J = 24 000 J
looking at its Greek
roots. Iso means ‘same’ The example above illustrates how energy flows in response
and thermo means to the minus-oneth law of thermodynamics, to achieve thermal
‘energy’ or ‘tempera- equilibrium. The impetus for energy flow is the equalization of
ture’, so a measure- temperature (via the zeroth law), so we say that the measurement
ment is isothermal is isothermal.
when performed at a We often want to perform thermodynamic studies isothermally
constant temperature.
because, that way, we need no subsequent corrections for inequal-
ities in temperature; isothermal measurements generally simplify
our calculations.

Why, when letting down a bicycle tyre, is the expelled
air so cold?

Thermodynamic work

When a fully inflated car tyre is allowed to deflate, the air streaming through the
nozzle is cold to the touch. The pressure of the air within the tyre is fairly high, so
opening the tyre valve allows it to leave the tyre rapidly – the air movement may even
cause a breeze. We could feel a jet of cold air on our face if we were close enough.
As it leaves the tyre, this jet of air pushes away atmospheric air, which requires
an effort. We say that work is performed. (It is a form of pres-
sure–volume work, and will be discussed in more depth later, in
Energy added to, or Section 3.2.)
work done on, a sys-
The internal energy of the gas must change if work is performed,
tem is positive.Energy
removed from, or work because U = q + w. It is unlikely that any energy is exchanged
so, in this simplistic example, we assume that q = 0.
done by, a system is
negative. Energy is consumed because work w is performed by the gas,
causing the energy of the gas to decrease, and the change in internal