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so. When this is recognized, it is unnecessary to write conversion factors as part of an
equation. Therefore, the conversion factor J will not be written in equations in this
book, it being understood that work and heat, for example, appearing in the same
equation must be expressed in the same units. Thus Eq. 1.40 becomes



Q
 L   or  ( Q  L )  0 (1.41)

We can then state the first law of thermodynamics as: For any cyclic process of a
closed system, the net work output of the system is equal to the net heat input.
The first law of thermodynamics is a far-reaching principle of nature which is induced
from the results of many experiments. It cannot be deduced or proved from any other
principles of nature. The inductive reasoning process, by which we take the results of a
finite number of experiments and extend them to cover all cases, always leaves some
room for doubt as to the value of its conclusions. With regard to its truth and range of
application, all we can say about the first law of thermodynamics is that many, many
experimental measurements are in accord with it and all attempts to find an exception to
it have so far failed.

Let the initial internal energy of system be U 1. Suppose the system interacts with
its surroundings by receiving heat Q and doing work L, and the internal energy attains
the final value U 2. We shall suppose that the quantities Q, L and (U 1 - U 2) are expressed
in the same units (joules). As the system received heat Q and spends energy W, the net
energy received by the system is (Q - L), and this must be equal to the increase in its
internal energy (U 1 - U 2), by the Law of Conservation of Energy. Hence, we get the
relation:

(Q - L) = (U 1 - U 2), or Q = ΔU - L, (1.42)

which expresses the First Law of Thermodynamics.

We must remember that:
 the sign of Q is positive when heat enters the system, and it is negative when work

is done on the system;
 the sign of L is positive when work is done by the system, and it is negative when
work is done on the system.
When the change in internal energy ΔU, heat transferred and work done are very
small quantities, we denote them by dU, dQ and dL respectively. We the write the
equation as:

dQ = dU - dL, (1.43)

which expresses the First Law of Thermodynamics in differential form.

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