Thermodynamics

It is the only physical theory of universal content concerning which I am convinced that, within the framework of the applicability of its basic concepts, it will never be overthrown.

Chemical energy stored by molecules can be released as heat during chemical reactions when a fuel like methane, cooking gas or coal burns in air. The chemical energy may also be used to do mechanical work when a fuel burns in an engine or to provide electrical energy through a galvanic cell like dry cell. Thus, various forms of energy are interrelated and under certain conditions, these may be transformed from one form into another. The study of these energy transformations forms the subject matter of thermodynamics. The laws of thermodynamics deal with energy changes of macroscopic systems involving a large number of molecules rather than microscopic systems containing a few molecules. Thermodynamics is not concerned about how and at what rate these energy transformations are carried out, but is based on initial and final states of a system undergoing the change. Laws of thermodynamics apply only when a system is in equilibrium or moves from one equilibrium state to another equilibrium state. Macroscopic properties like pressure and temperature do not change with time for a system in equilibrium state. In this unit, we would like to answer some of the important questions through thermodynamics, like:

How do we determine the energy changes involved in a chemical reaction/process? Will it occur or not?

What drives a chemical reaction/process?

To what extent do the chemical reactions proceed?

Albert Einstein

However, the entire universe other than the system is not affected by the changes taking place in the system. Therefore, for all practical purposes, the surroundings are that portion of the remaining universe which can interact with the system. Usually, the region of space in the neighbourhood of the system constitutes its 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. 5.1).

Note that the system may be defined by physical boundaries, like beaker or test tube, or the system may simply be defined by a set of Cartesian coordinates specifying a particular volume in space. It is necessary to think of the system as separated from the surroundings by some sort of wall which may be real or imaginary. The wall that separates

* We could have chosen only the reactants as system then walls of the beakers will act as boundary.

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.

1. Open System In an open system, there is exchange of energy and matter between system and surroundings [Fig. 5.2 (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.

2. Closed System In a closed system, there is no exchange of matter, but exchange of energy is possible between system and the surroundings [Fig. 5.2 (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.

3. Isolated System

In an isolated system, there is no exchange of energy or matter between the system and the surroundings [Fig. 5.2 (c)]. The presence of reactants in a thermos flask or any other closed insulated vessel is an example of an isolated system.

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.

These systems are classified accordingly as you have already studied in section 5.1.2.

(a) Work 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 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 adiabatic process. 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. 5.3).

One way: We do some mechanical work, say 1 kJ, by rotating a set of small paddles and thereby churning water. Let the new state be called B state and its temperature, as $T_B$. It is found that $T_B>T_A$ and the change in temperature, $\Delta T=T_B-T_A$. Let the internal energy of the system in state B be $U_B$ and the change in internal energy, $\Delta U=U_B-U_A$. Second way: We now do an equal amount (i.e., 1 kJ) electrical work with the help of an immersion rod and note down the temperature change. We find that the change in temperature is same as in the earlier case, say, $T_B-T_A$.

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 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, $w_{ad}$ 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., $\Delta U=U_2-U_1=w_{ad}$ Therefore, internal energy, $U$, of the system is a state function. By conventions of IUPAC in chemical thermodynamics. The positive sign expresses that $w_{ad}$ 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, $w_{ad}$ will be negative because internal energy of the system decreases. Can you name some other familiar state functions? Some of other familiar state functions are $V$, $p$, and $T$. For example, if we bring a change in temperature of the system from $25{}^{\circ }\text{C}$ to $35{}^{\circ }\text{C}$, the change in temperature is $35{}^{\circ }\text{C}-25{}^{\circ }\text{C}=+10{}^{\circ }\text{C}$, whether we go straight up to $35{}^{\circ }\text{C}$ or we cool the system for a few degrees, then take the system to the final temperature. Thus, $T$ is a state function and the change in temperature is independent of

* Earlier negative sign was assigned when the work is done on the system and positive sign when the work is done by the system. This is still followed in physics books, although IUPAC has recommended the use of new sign convention.

the route taken. Volume of water in a pond, for example, is a state function, because change in volume of its water is independent of the route by which water is filled in the pond, either by rain or by tubewell or by both.

(b) Heat 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 (the same initial and final states as before in section 5.1.4 (a) by transfer of heat through thermally conducting walls instead of adiabatic walls (Fig. 5.4).

We take water at temperature, $T_A$ in a container having thermally conducting walls, say made up of copper and enclose it in a huge heat reservoir at temperature, $T_B$. The heat absorbed by the system (water), $q$ can be measured in terms of temperature difference, $T_B-T_A$. 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.

(c) The general case Let us consider the general case in which a change of state is brought about both by doing work and by transfer of heat. We write change in internal energy for this case as: $\Delta U=q+w$ (5.1)

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 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.

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) $w$ 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?

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

inside becomes equal to $p_{ex}$. Let this change be achieved in a single step and the final volume be $V_f$. During this compression, suppose piston moves a distance, $l$ and is cross-sectional area of the piston is $A$ [Fig. 5.5(a)]. then, volume change $=l\times A=\Delta V=(V_f-V_i)$

We also know, $\text{pressure}=\frac{\text{force}}{\text{area}}$