THERMODYNAMICS 307
What are the ways of changing internal
energy of a system ? Consider again, for
simplicity, the system to be a certain mass of
gas contained in a cylinder with a movable
piston as shown in Fig. 12.4. Experience shows
there are two ways of changing the state of the
gas (and hence its internal energy). One way is
to put the cylinder in contact with a body at a
higher temperature than that of the gas. The
temperature difference will cause a flow of
energy (heat) from the hotter body to the gas,
thus increasing the internal energy of the gas.
The other way is to push the piston down i.e. to
do work on the system, which again results in
increasing the internal energy of the gas. Of
course, both these things could happen in the
reverse direction. With surroundings at a lower
temperature, heat would flow from the gas to
the surroundings. Likewise, the gas could push
the piston up and do work on the surroundings.
In short, heat and work are two different modes
of altering the state of a thermodynamic system
and changing its internal energy.
The notion of heat should be carefully
distinguished from the notion of internal energy.
Heat is certainly energy, but it is the energy in
transit. This is not just a play of words. The
distinction is of basic significance. The state of
a thermodynamic system is characterised by its
internal energy, not heat. A statement like ‘a
gas in a given state has a certain amount of
heat’ is as meaningless as the statement that
‘a gas in a given state has a certain amount
of work’. In contrast, ‘a gas in a given state
has a certain amount of internal energy’ is a
perfectly meaningful statement. Similarly, the
statements ‘a certain amount of heat is
supplied to the system’ or ‘a certain amount
of work was done by the system’ are perfectly
meaningful.
To summarise, heat and work in
thermodynamics are not state variables. They
are modes of energy transfer to a system
resulting in change in its internal energy,
which, as already mentioned, is a state variable.
In ordinary language, we often confuse heat
with internal energy. The distinction between
them is sometimes ignored in elementary
physics books. For proper understanding of
thermodynamics, however, the distinction is
crucial.
12.5 FIRST LAW OF THERMODYNAMICS
We have seen that the internal energy U of a
system can change through two modes of energy
transfer : heat and work. Let
∆Q = Heat supplied to the system by the
surroundings
∆W = Work done by the system on the
surroundings
∆U = Change in internal energy of the system
The general principle of conservation of
energy then implies that
∆Q = ∆U + ∆W (12.1)
i.e. the energy (∆Q) supplied to the system goes
in partly to increase the internal energy of the
system (∆U) and the rest in work on the
environment (∆W). Equation (12.1) is known as
the First Law of Thermodynamics. It is simply
the general law of conservation of energy applied
to any system in which the energy transfer from
or to the surroundings is taken into account.
Let us put Eq. (12.1) in the alternative form
∆Q – ∆W = ∆U (12.2)
Now, the system may go from an initial state
to the final state in a number of ways. For
example, to change the state of a gas from
(P
1
, V
1
) to (P
2
, V
2
), we can first change the
volume of the gas from V
1
to V
2
, keeping its
pressure constant i.e. we can first go the state
(P
1
, V
2
) and then change the pressure of the
gas from P
1
to P
2
, keeping volume constant, to
take the gas to (P
2
, V
2
). Alternatively, we can
first keep the volume constant and then keep
the pressure constant. Since U is a state
variable, ∆U depends only on the initial and
final states and not on the path taken by the
gas to go from one to the other. However, ∆Q
and ∆W will, in general, depend on the path
taken to go from the initial to final states. From
the First Law of Thermodynamics, Eq. (12.2),
it is clear that the combination ∆Q – ∆W, is
however, path independent. This shows that
if a system is taken through a process in which
∆U = 0 (for example, isothermal expansion of
an ideal gas, see section 12.8),
∆Q = ∆W
i.e., heat supplied to the system is used up
entirely by the system in doing work on the
environment.