Page 120 - Physical chemistry understanding our chemical world

INTRODUCTION TO THERMODYNAMICS: INTERNAL ENERGY 87

Work and energy can be considered as interchangeable: we per-
Work done on asystem
form work whenever energy powers a physical process, e.g. to
increases its energy,
propel a car or raise a spoon to the mouth. The work done on so U is positive. Work
a system increases its energy, so the value of U increases, itself done by asystemcor-
causing U to be positive). Work done by a system corresponds responds to a negative
to a negative value of U. value of U.

Why does a sausage become warm when placed
in an oven?

Isothermal changes in heat and work

At first sight, the answer to our title question is obvious: from the minus-oneth law
of thermodynamics, heat travels from the hot oven to the cold(er) item of food we
place in it. Also, from the zeroth law, thermal equilibrium is attained only when the
sausage and the oven are at the same temperature. So the simplest answer to why
a sausage gets hot is to say the energy content of the sausage (in the form of heat)
increases, causing its internal energy to rise. And, yet again, we see how the simplest
test of an increasing internal energy is an increased temperature.
We can express this truth by saying the sausage gets warmer as
the magnitude of its internal energy increases; so, from Equation Care:inthe past,
(3.1), U = U (final) − U (initial) , hence U = U (after heating) − Equation (3.5) was
U (before heating) . We see how the value of U is positive since often written as U =
U (after heating) >U (before heating) . q − w, where the minus
But we can now be more specific. The internal energy U changes sign is intended to
in response to two variables, work w and heat energy q, as defi- show how the internal
energy decreases fol-
ned by lowing work done by
U = q + w (3.5)
a system. We will use
Equation (3.5), which
We have already met the first law of thermodynamics. Equa- is the more usual form.
tion (3.5) here is the definitive statement of this law, and is ex-
pressed in terms of the transfer of energy between a system and its
environment. In other words, the magnitude of U is the sum of
the changes in the heat q added (or extracted) from a system, and
the work w performed by (or done to) it.
Care: The symbol of
The internal energy can increase or decrease even if one or other the joule is J. A small ‘j’
of the two variables, q and w, remains fixed. Although the sausage does not mean joules;
does no work w in the oven, the magnitude of U increases it represents another
because the food receives heat energy q from the oven. variable from a com-
pletely different branch
Worked Example 3.3 What is the energy of the sausage after heat- of physical chemistry.
ing, if its original energy is 4000 J, and 20 000 J is added to it?
No work is done, so w = 0.