The first law of thermodynamics and related concepts

 This page is devoted to the first law of thermodynamics, the variables invovled and to the details of the concepts related to it.

The theory, and applications, of the laws of thermodynamics are common to different fields of knowledge so that different approaches can be found. However, for chemistry and chemical engineering the books physical chemistry and thermodynamical chemistry are a very good. source of exercises and examples nearer to these fields of study.

1rst law of thermodynamics

For short, this can be written as,

$\Delta U= Q + w$        Eq. (01)

where $U$ is the internal energy, $\Delta U$ is the change of the internal energy due to a thermodynamical process, $Q$ is the heat or thermal energy, that can be taken or supplied to the system, and $w$ is the work, done on or by the system.

Fig. 1. 1rst law of thermodynamics

About the units

Since this is an equation and every equation must be consistent in its units it is natural that all quantities in Eq. (01) have the same units. For, example in SI units $U$, $Q$ and $w$ are given in joules (J).

It is not uncommon to find authors using calories (cal) as units for the heat $Q$. If that is the case, the units of all quantities must be the same.

The nature of the internal energy $U$

The internal energy $U$ is different from other types of common energies such as: momentum or electrical, for example. The internal energy $U$ is related to the molecules forming the matter. Thus, the kind of energy $U$ is about are the following,

• the kinetic energy of molecules,
• the potential energy due to interactions among the molecules, and
• the kinetic and potential energy of the internal components of the molecules, such as the electrons for example.

Nature of $Q$

$Q$ represents the heat that the system may give to its surroundings or that the surroundings may supply to the system. A practical example of the first case is found when a hot cup of coffee is placed inside the fridge because the hot liquid gives its thermal energy to the cool air surrounding it. An example of the second case could be the water of a lake which becomes warmer during summer days due to the higher temperatures in that season.

From the view of chemistry a chemical reaction occurring inside a flask or a reactor, for example, may require heat in order to occur. On the other hand, the chemical reaction itself may also release heat to the environment. Then, one can understand the role of heat $Q$.

Some comments on the work $w$

Finally, $w$ resembles to a statement of classical mechanics,

Fig. 2 Classical concept for work

which implies an applied force and a displacement of something. For thermodynamical purposes the concept in Fig. 2 can be rewritten as follows,

Fig. 3 Thermodynamical interpretation of work

which now implies that the work can be done in two directions: by increasing or by decreasing the pressure, so that the volume expands or compresses as well.

Trying to get a better understanding of this and establishing a proper technical language one would say:

• that the system may perform a work on its surroundings. This is, according to IUPAC, usually represented as $-w$;
• for the other case, that the surrounding performs a work on the system. Again, according to IUPAC, this is expressed as $w$.

You should notice that the minus sign is assigned to the variable rather than to the numerical values.

Fig. 4 A sketch representing a system, as the whole inside the reactor, the surroundings, as anything outside the reactor, and its boundary, as the rector walls.

For chemical engineers and chemists the work will usually be done, in any direction, due to a chemical reaction or because of it.

Types of thermodynamical processes

Thermodynamical processes can be organized according to the changing or constant behavior of some variables. These are:

Isothermal process

Also called process at constant temperature. This is that while temperature $T$ remains constant the pressure $P$ and volume $V$ may change.

Isobaric process

Also called process at constant pressure. This is that while pressure $P$ remains constant the temperature $T$ and volume $V$ may change.

Isochoric process

Also called process at constant volume. This is that while volume $V$ remains constant the temperature $T$ and pressure $P$ may change.

Also, there exist another set of two categories for thermodynamical processes. These are usually related to the work $w$. Before, talking about these other types of processes another concept needs to be introduced.

Concept of: Thermodynamical equilibrium

This refers to a state of the system in which all its state functions have contant values. For short this caould be interpreted as if the system remained unchanged in time. From the point of view of the first law of thermodynamics it would mean that $\Delta U=0$.

Remember that $Q$ and $w$ are not thermodyamical state funtions.

 

The next two types of thermodynamical processes are outlined as follows:

Irreversible thermodynamical  processes

This is one in which the changes in the system may occur slow or very fast with the condition that the system is set out of equilibrium.

Since a thermodynamical process implies, for example, two different states of the system (state-1 and state-2), and irreversible process would mean that these two states are so different that it is not possible to go back from state-1 to state-2. Let us say that the exact position of the molecules of the gas can not be retraced. The change was so dramatic that the process can not be reversed.

Reversible thermodynamical  processes

A reversible process implies a tricky idea. For a process to be reversible the system never must go out of its thermodynamical equilibrium.

Then, how can you perform a thermodynamical process such that it never goes out of equilibrium? Easy, the changes should occur at a very slow pace or, as it is referred in the mathematical language, of infinitesimal size. Another wy of saying it is that the changes would not be noticeable for the human eye or that you would need a very accurate and expensive instruments to measure any change.

The advantage of infinitesimal changes is that the state-1 of the system can be recoverd from state-2.

Process with adition of heat (no work)

If no work $w$ is done by or on the system, then the equation of the first law of thermodynamics reduces to,

Fig. 5 First law of thermodynamics for the case of no work done by or on the system.

This would mean that thermal energy $Q$ is added to the system or extracted from the system without work done by or on the system. In other words, neither expansion nor compression is occurring.

Process where work is being done  without heat transfer

For this case, the equation for the first law of thermodynamics becomes,

Fig. 6 First law of thermodynamics for the case of no heat being added to the system or extracted from it.

Here, there is expansion or compression but no thermal energy is flowing in any direction.

Any question? Write in the comments and I shall try to help.

Other stuff of interest

• Some basic concepts on thermodynamics
• Who was Clausius?
• Units conversion
• Composition variables in mixtures
• About PID controllers
• Ways to control a process
• About pilot lights
• Solving the Colebrook equation

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Ildebrando.