5.1 Thermodynamic Terms

We are interested in chemical reactions and the energy changes accompanying them. For this, we need to know certain thermodynamic terms. These are discussed below.

The System and the Surroundings

A system in thermodynamics refers to that part of the universe in which observations are made and the remaining universe constitutes the surroundings. The surroundings include everything other than the system. The system and the surroundings together constitute the universe.

The universe = The system + The surroundings

For example, if we are studying the reaction between two substances A and B kept in a beaker, the beaker containing the reaction mixture is the system and the room where the beaker is kept is the surroundings (Fig. 6.1).be real or imaginary. The wall that separates the system from the surroundings is called boundary. This is designed to allow us to control and keep track of all movements of matter and energy in or out of the system.

Thermodynamic System

A collection of an extremely large number of atoms or molecules confined within certain boundaries such that it has certain values of pressure \((P)\), volume \((V)\) and temperature \((T)\) is called a thermodynamic system.

System: A system is a region containing energy and/or matter that is separated from its surroundings by arbitrarily imposed walls or boundaries.

Surroundings: Everything that interacts with the system (Everything outside the system that has a direct influence on the behaviour of the system is known as a surrounding.)

System boundary: A boundary is a closed surface surrounding a system through which energy and mass may enter or leave the system.

For example, consider a closed beaker with liquid inside as shown below. The liquid inside the beaker is the system, while the outline of the beaker represents the boundary of the system. And matter outside the system and boundary is called its surroundings.

Types of Thermodynamic System

Thermodynamic systems are classified according to the movements of matter and energy in or out of the system. There are three types of systems:

• Open System: In an open system, there is exchange of energy and matter between system and surroundings [Fig. 6.2 (a)]. The presence of reactants in an open beaker is an example of an open system*. Here the boundary is an imaginary surface enclosing the beaker and reactants.  In an open system, the mass and energy both may be transferred between the system and surroundings. A steam turbine is an example of an open system.

• Closed System: In a closed system, there is no exchange of matter, but exchange of energy is possible between system and the surroundings [Fig. 6.2 (b)]. The presence of reactants in a closed vessel made of conducting material e.g., copper or steel is an example of a closed system. Across the boundary of the closed system, the transfer of energy takes place but the transfer of mass doesn’t take place. Refrigerator and compression of gas in the piston-cylinder assembly are examples of closed systems.

• Isolated System: In an isolated system, there is no exchange of energy or matter between the system and the surroundings [Fig. 6.2 (c)]. The presence of reactants in a thermos flask or any other closed-insulated vessel is an example of an isolated system. An isolated system cannot exchange energy and mass with its surroundings. The universe is considered an isolated system.

Thermodynamic Process

A system undergoes a thermodynamic process when there is some energetic change within the system that is associated with changes in pressure, volume and internal energy. There are four types of thermodynamic processes that have their unique properties, and they are:

• Adiabatic Process: A process where no heat transfer into or out of the system occurs.
• Isochoric Process: A process where no change in volume occurs and the system does no work.
• Isobaric Process: A process in which no change in pressure occurs.
• Isothermal Process: A process in which no change in temperature occurs.

The State of the System

The system must be described in order to make any useful calculations by specifying quantitatively each of the properties such as its pressure \((P)\), volume \((V)\), and temperature ( \(T\) ) as well as the composition of the system. The state of a thermodynamic system is described by its measurable or macroscopic (bulk) properties. We can describe the state of a gas by quoting its pressure \((P)\), volume \((V)\), temperature \((T)\), amount \((n)\), etc. Variables like \(P, V, T\) are called state variables or state functions because their values depend only on the state of the system and not on how it is reached. The state of the surroundings can never be completely specified; fortunately, it is not necessary to do so.

The Internal Energy as a State Function

When we talk about our chemical system losing or gaining energy, we need to introduce a quantity which represents the total energy of the system. It may be chemical, electrical, mechanical or any other type of energy you may think of, the sum of all these is the energy of the system. In thermodynamics, we call it the internal energy, \(U\) of the system, which may change, when

• heat passes into or out of the system,
• work is done on or by the system,
• matter enters or leaves the system.

Work

The work done by a system or on a system during a process depends not only on the system’s starting and final states but also on the path chosen for the process. When a force acting on a system moves the body in its own direction, work has been done. Force and displacement combine to create the work (W) that is done to or by a system.

Let us first examine a change in internal energy by doing work. We take a system containing some quantity of water in a thermos flask or in an insulated beaker. This would not allow the exchange of heat between the system and surroundings through its boundary and we call this type of system as adiabatic. The manner in which the state of such a system may be changed will be called the adiabatic process. The adiabatic process is a process in which there is no transfer of heat between the system and surroundings. Here, the wall separating the system and the surroundings is called the adiabatic wall (Fig 6.3).

Let us bring the change in the internal energy of the system by doing some work on it. Let us call the initial state of the system as state \(\mathrm{A}\) and its temperature as \(T_{\mathrm{A}}\). Let the internal energy of the system in state A be called \(U_{\mathrm{A}}\). We can change the state of the system in two different ways.

One way: We do some mechanical work, say \(1 \mathrm{~kJ}\), by rotating a set of small paddles and thereby churning water. Let the new state be called B state and its temperature, as \(T_{\mathrm{B}}\). It is found that \(T_{\mathrm{B}}>T_{\mathrm{A}}\) and the change in temperature, \(\Delta T=T_{\mathrm{B}}-T_{\mathrm{A}}\). Let the internal energy of the system in state \(\mathrm{B}\) be \(U_{\mathrm{B}}\) and the change in internal energy, \(\Delta U=U_{\mathrm{B}}-U_{\mathrm{A}}\).

Second way: We now do an equal amount (i.e., \(1 \mathrm{~kJ}\) ) electrical work with the help of an immersion rod and note down the temperature change. We find that the change in temperature is the same as in the earlier case, say, \(T_{\mathrm{B}}-T_{\mathrm{A}}\).

In fact, the experiments in the above manner were done by J. P. Joule between 1840-50 and he was able to show that a given amount of work done on the system, no matter how it was done (irrespective of the path) produced the same change of state, as measured by the change in the temperature of the system.

So, it seems appropriate to define a quantity, the internal energy \(U\), whose value is characteristic of the state of a system, whereby the adiabatic work, \(\mathrm{w}_{\mathrm{ad}}\) required to bring about a change of state is equal to the difference between the value of \(U\) in one state and that in another state, \(\Delta U\) i.e.,
\(
\Delta U=U_2-U_1=\mathrm{w}_{\mathrm{ad}}
\)

Therefore, internal energy, \(U\), of the system is a state function.

By conventions of IUPAC in chemical thermodynamics. The positive sign expresses that \(\mathrm{w}_{\mathrm{ad}}\) is positive when work is done on the system and the internal energy of system increases. Similarly, if the work is done by the system, \(\mathrm{w}_{\mathrm{ad}}\) will be negative because the internal energy of the system decreases.

Heat

Heat is energy that is transmitted between objects or systems as a result of a temperature difference. Heat is conserved energy, which means it cannot be created or destroyed. However, it can be moved from one location to another. Additionally, heat can be transformed into and out of various types of energy.

We can also change the internal energy of a system by transfer of heat from the surroundings to the system or vice-versa without expenditure of work. This exchange of energy, which is a result of temperature difference is called heat, \(q\). Let us consider bringing about the same change in temperature by the transfer of heat through thermally conducting walls instead of adiabatic walls (Fig. 6.4).

We take water at temperature, \(T_{\mathrm{A}}\) in a container having thermally conducting walls, say made up of copper and enclose it in a huge heat reservoir at temperature, \(T_{\mathrm{B}}\). The heat absorbed by the system (water), \(q\) can be measured in terms of temperature difference, \(T_{\mathrm{B}}-T_{\mathrm{A}}\). In this case change in internal energy, \(\Delta U=q\), when no work is done at constant volume.

By conventions of IUPAC in chemical thermodynamics. The \(q\) is positive, when heat is transferred from the surroundings to the system and the internal energy of the system increases and \(q\) is negative when heat is transferred from system to the surroundings resulting in decrease of the internal energy of the system.

The general case

Let us consider the general case in which a change of state is brought about both by doing work and by the transfer of heat. We write change in internal energy for this case as:
\(
\Delta U=q+\mathrm{w} \dots(6.1)
\)

For a given change in state, \(q\) and \(w\) can vary depending on how the change is carried out. However, \(q+\mathrm{w}=\Delta U\) will depend only on the initial and final state. It will be independent of the way the change is carried out. If there is no transfer of energy as heat or as work (isolated system) i.e., if \(\mathrm{w}=0\) and \(q=0\), then \(\Delta U=0\).
The equation 6.1 i.e., \(\Delta U=q+\mathrm{w}\) is mathematical statement of the first law of thermodynamics, which states that
The energy of an isolated system is constant. It is commonly stated as the law of conservation of energy i.e., energy can neither be created nor be destroyed.

Note: There is a considerable difference between the character of the thermodynamic property energy and that of a mechanical property such as volume. We can specify an unambiguous (absolute) value for volume of a system in a particular state, but not the absolute value of the internal energy. However, we can measure only the changes in the internal energy, \(\Delta U\) of the system.

Example 6.1: Express the change in internal energy of a system when
(i) No heat is absorbed by the system from the surroundings, but work (w) is done on the system. What type of wall does the system have?
(ii) No work is done on the system, but \(q\) amount of heat is taken out from the system and given to the surroundings. What type of wall does the system have?
(iii) \(\mathrm{w}\) amount of work is done by the system and \(q\) amount of heat is supplied to the system. What type of system would it be?

Answer: (i) \(\Delta U=\mathrm{w}_{\mathrm{ad}}\), wall is adiabatic
(ii) \(\Delta U=-q\), thermally conducting walls
(iii) \(\Delta U=q-\mathrm{w}\), closed system.