Page 53 - Instant notes

The first law 39

A and B are fixed quantities, altitude is
therefore a state function. The amount
of work done and the distance traveled
in climbing from A to B depend upon
the path. The work and the distance
traveled are therefore path functions.

and work respectively, and negative if energy is lost from the system as heat or work.
Work and heat are path functions, since the amount of work done or heat lost depends
not on the initial and final states of the system, but on how that final state is reached. In
changing the internal energy of a system, the amount of energy lost as heat or as work,
depends upon how efficiently the energy is extracted. Hence some cars travel further on a
given amount of petrol than others depending on how efficiently the internal energy of
the petrol is harnessed to do work.

Work

There are a limited number of ways in which energy may be exchanged in the form of
work. The most commonly encountered of these is pressure-volume or pV work.
Electrical work may also be performed by a system (see Topics E3, E4 and E5), and this
may be accounted for by including an appropriate term, but in most cases this may be
discounted. When a reaction releases a gas at a constant external pressure, p ex work is
done in expanding, ‘pushing back’, the surroundings. In this case, the work done is given
by:
w=−p ex.∆V

and so the change in internal energy ∆U in such a reaction is:
∆U=−p ex.∆V+q

If a reaction is allowed to take place in a sealed container at fixed volume then ∆V=0, and
so the expression for ∆U reduces to ∆U=q. This is the principle of a bomb calorimeter.
A bomb calorimeter is a robust metal container in which a reaction takes place (often
combustion at high oxygen pressure). As the reaction exchanges heat with the
surroundings (a water bath, for example), the temperature of the surroundings changes.
Calibration of the bomb using an electrical heater or standard sample allows this
temperature rise to be related to the heat output from the reaction and the value of q, and
hence ∆U, obtained.

Heat capacity

When energy is put into a system, there is usually a corresponding rise in the temperature
of that system. Assuming that the energy is put in only as heat, then the rise in