First Law of Thermodynamics: Explanation

The First Law of Thermodynamics states the relationship between heat and work and the concept of internal energy. Energy, like matter, is always conserved, meaning it cannot be created or destroyed but can be changed into different forms.

It is very important for the students to first understand the basic concept behind this theory and then read it thoroughly. Many energy transfers and conversions occur whenever a system undergoes a change resulting from the interaction of heat, work, and internal energy. However, there is no net change in total energy throughout these exchanges. This article will learn about the definition and limitations of the first law of thermodynamics.

First Law of Thermodynamics Definition

The first law of thermodynamics is simply the law of conservation of energy which states that energy can neither be created nor destroyed, although it can be converted from one form to another.

The law may also be stated in the following ways.

1. The total energy of an isolated system remains constant, although it can undergo a change from one form to another.
2. Whenever a quantity of some form of energy disappears, an exactly equivalent amount of some other form of energy must be produced.
3. It is impossible to construct a perpetual motion machine that would produce work continuously without consuming energy (Helmholtz, \(1847\)).
4. For a system in contact with its surroundings, the sum of the energies of the system and the surroundings at a particular time remains constant. However, differently, it may be shared between the two.
5. The equivalence of heat and mechanical work established by Joule also follows as a conference of the first law of thermodynamics. Suppose there is no equivalence between heat and work. Now suppose \({\rm{Q}}\) calories of heat are converted into mechanical work, and the same amount of work done is converted back into a certain amount of heat say \({\rm{Q}}’\). If \({\rm{Q}} \ne {\rm{Q}}’\) then \({\rm{Q}} > {\rm{Q}}’\) or \({\rm{Q}} < {\rm{Q}}’.\) This indicates that although the original state of the matter has been restored, a certain amount of energy has been created or destroyed, which is against the law of thermodynamics. Hence there must exist an exact equivalence between heat and mechanical work.
6. Einstein in \(1905\) established the fact that energy can be produced by the destruction of mass and the two quantities are related to each other by the expression
   \({\rm{E}} = {\rm{m}}{{\rm{c}}^2}\)

Where E is the energy produced by the destruction of mass m, and c is the velocity of light. This is not in contradiction with the first law of thermodynamics since mass in its generalized form may be considered as some kind of potential energy. The law of conservation of mass and the law of conservation of energy are combined together to give the law of conservation of mass and energy. The modified law may be stated as follows.

‘The total mass and energy of an isolated system remain constant in chemical thermodynamics.’

However, in ordinary chemical reactions, accompanied by the evolution of heat, the change in mass is so small that it is almost undetectable on any chemical balance. Hence the above relationship is of no significance in chemical thermodynamics.

Practice Exam Questions

Mathematical Formulation of the First Law of Thermodynamics

The internal energy of a system can be increased in two ways:

1. By supplying heat to the system,
2. By doing work on the system.

Suppose the initial internal energy of the system \( = {{\rm{E}}_1}\)

If it absorbs heat \({\rm{q}}\), its internal energy will become \( = {{\rm{E}}_1} + {\rm{q}}\)

If further work \({\rm{w}}\) is done on the system, the internal energy will further increase and become \( = {{\rm{E}}_1} + {\rm{q}} + {\rm{w}}\). Let us call this final internal energy as \({{\rm{E}}_2}\). Then \({{\rm{E}}_2} = {{\rm{E}}_1} + {\rm{q}} + {\rm{w}}\) or \({{\rm{E}}_2} – {{\rm{E}}_1} = {\rm{q}} + {\rm{w}}\)

Or \(\Delta {\rm{E}} = {\rm{q}} + {\rm{w}} \ldots \ldots \ldots (1)\)

This equation is the mathematical formulation of the first law of thermodynamics.

If the work done is the work of expansion, then \({\rm{w}} = \,- {\rm{P\Delta V}}\), where \({\rm{\Delta V}}\) is the change in volume and \({\rm{P}}\) is the external pressure. Equation \({\rm{(i)}}\) can then be written as

\({\rm{\Delta E}} = {\rm{q}} – {\rm{P\Delta V}}\) or \({\rm{q}} = {\rm{\Delta E}} + {\rm{P\Delta V}}………….{\rm{(2)}}\)

Two interesting results follow from the mathematical formulation of the first law of thermodynamics, as under

1. Neither \({\rm{q}}\) nor w is a state function, yet the quantity \({\rm{q}} + {\rm{w}}( = {\rm{\Delta E}})\) is a state function (because \({\rm{\Delta E}}\) is a state function).
2. Internal energy \({\rm{(E)}}\) of an ideal gas is a function of temperature. Hence, for an ideal gas undergoing an isothermal change, \({\rm{\Delta E}} = 0.\) Hence, \({\rm{q}} =\, – {\rm{w}}\), i.e., the heat absorbed by the system is equal to work done by the system.

During an adiabatic change, \({\rm{q}} = 0\) so that \({\rm{\Delta E}} = {{\rm{w}}_{{\rm{adiabatic }}}}\)

Special Forms of the First Law of Thermodynamics

Under special conditions, equation \(\left( 1 \right)\) for the first law of thermodynamics is modified as below.

1. For a cyclic process resulting in its original state, that is, for a process involving isothermal expansion of an ideal gas,
   \({\rm{\Delta E}} = 0\)
   \(\therefore \,{\rm{q}} = {\rm{w}}\)
   i.e., the work done by the gas is exactly equal to the heat absorbed.
2. For a process in which volume remains constant, no work of expansion is done, i.e., \({\rm{W}} = 0.\) Hence the equation \(\left( 1 \right)\) for the first law of thermodynamics becomes
   \({\rm{\Delta E}} = {{\rm{Q}}_{\rm{v}}}\)  (\({\rm{v}}\) indicates constant volume)
   Since \({\rm{\Delta E}}\) is a state function, \({{\rm{Q}}_{\rm{v}}}\) also must be a state function.
   Thus, at constant volume, the increase in the internal energy of the gas (as indicated by its rise in temperature) is equal to the heat absorbed.
3. For an adiabatic expansion process, i.e. when no heat is gained or lost to the surroundings, which is possible when the system is well insulated,
   \({\rm{dQ}} = 0\)
   \(\therefore \,{\rm{\Delta E}} = – {{\rm{W}}_{\rm{q}}}\)  (\({\rm{q}}\) indicates constant heat)

Thus, in such cases, the decrease in internal energy is exactly equal to the work done. The negative sign shows that work is done by the system on the surroundings.

Internal Energy is a State Function

The internal energy is a state function that is when a process occurs, the change in its value depends only upon its values in the initial and final states and is independent of the path by which the change is brought about.

Consider a system having a particular pressure, volume and temperature represented by point \({\rm{A}}\) (initial state) in the figure. Suppose the pressure, volume and temperature are changed so that the system is brought to point \({\rm{B}}\) (final state) by path \({\rm{I}}\). Let the change in internal energy of the system during the conversion of \({\rm{A}}\) to \({\rm{B}}\) is \({\rm{\Delta E}}\) 

Further, suppose \({\rm{B}}\) is converted back to \({\rm{A}}\) but through another path, path \({\rm{II}}\), the change in internal energy during this process (say \({\rm{\Delta E}}\)) must be equal in magnitude to that involved in the path \({\rm{I}}\). If the energy changes involved in paths \({\rm{I}}\) and \({\rm{II}}\) are not the same in magnitude, then suppose by the path \({\rm{I}}\) is greater than the decrease in internal energy along path \({\rm{II}}\), i.e., \({\rm{\Delta E}} > {\rm{\Delta E’}}\).

Then by a coupling of these two processes,
\({\rm{A}}\mathop \to \limits^{{\rm{ Path I}}} {\rm{B}}\mathop \to \limits^{{\rm{ Path II}}} {\rm{A}}\)

The system would return to its initial state to create a certain amount of energy equal to \({\rm{\Delta E – \Delta E’}}\). By repeating the same cycle repeatedly, energy would be generated continuously, and a perpetual motion machine would be possible, contrary to the first law of thermodynamics. Hence \({\rm{\Delta E = \Delta E’}}\).

Thus, we can say that energy change accompanying a process depends upon the initial and the final states of the system and is independent of the path by which these changes are brought about.

The two important points about internal energy are worth noting:

1. The internal energy depends upon the quantity of the substance present in the system. Hence, it is an extensive property.
2. The internal energy of ideal gases is a function of temperature only. Hence in isothermal processes (processes carried out at constant temperature), there is no change in internal energy, i.e., \({\rm{\Delta E = }}0\)

Work and Heat are Path Functions

Let a system changes from state \({\rm{A}}\) to state \({\rm{B}}\). This may be done by following different paths, as shown in the following figures.

Let us confine ourselves to the work of expansion only. We know that work done for a small change in volume \({\rm{dV}}\) is \({\rm{P\, dV}}\), where \({\rm{P}}\) is the external pressure. Thus, the total work done is the sum of \({\rm{P\, dV}}\) terms which is equivalent to the area under the curve in the \({\rm{P}} – {\rm{V}}\) diagram.

Since the areas (or the \({\rm{P\, dV}}\) terms) under the curves in the above three figures are different, work done in the three paths will be different. Hence, we can say that work is a path function, i.e., its value does not depend upon the initial and final states of the system but depends upon the path by which this change is brought about.

Heat is also a path function and not a state function. It can directly be realised from the mathematical formulation of the first law of thermodynamics, viz.

\({\rm{\Delta E}} = {\rm{Q}} – {\rm{W}}\)

\({\rm{\Delta E}}\) is a definite quantity. if \({\rm{W}}\) is not a definite quantity, \({\rm{Q}}\) cannot be a definite quantity. It is interesting to note that neither \({\rm{Q}}\) nor \({\rm{W}}\) is a state function, yet the quantity \({\rm{Q}} – {\rm{W}}\) (i.e., \({\rm{\Delta E}}\)) is a state function.

Limitations of the First Law of Thermodynamics

A major limitation of the first law of thermodynamics is that it merely indicates an exact equivalence between the various forms of energies involved in any process. Still, it provides no information concerning the spontaneity or feasibility of the process, i.e., whether the process is possible or not.

For example, the first law does not indicate whether heat can flow from a cold end to a hot end or not. It tells us that if this process occurred, the heat energy gained by one end would be exactly equal to that lost by the other end. Similarly, the first law does not tell whether gas can diffuse from low pressure to high pressure, whether water can itself run uphill or not, etc.

Summary

Thermodynamics can be understood with the help of certain laws. The simplest of them is the first law. According to the first law of thermodynamics, the energy in a process may be transformed from one form into another, but it is neither created nor destroyed. The first law of thermodynamics is known as the law of conservation of energy.
This article will learn about the definition of the first law of thermodynamics, the mathematical formulation of the first law of thermodynamics, and its limitations.

FAQs

Q.1. What does the first law of thermodynamics say?
Ans: The first law of thermodynamics is simply the law of conservation of energy which states that energy can neither be created nor destroyed. However, it may be converted from one form to another.

Q.2. What are the 1st, 2nd, and 3rd laws of thermodynamics?
Ans: The first law of thermodynamics states that the total energy of the universe (i.e., the system and the surroundings) remains constant. However, it may undergo a transformation from one form to the other.
The second law of thermodynamics states that the entropy of any isolated system always increases.
The entropy of perfectly crystalline solid approaches zeroes as the temperature approaches absolute zero.

Q.3. Who gave the first law of thermodynamics?
Ans: The first law of thermodynamics was given by Robert Mayer and Helmholtz.

Q.4. What is the application of the First Law of Thermodynamics?
Ans: In an isothermal process, the temperature of an ideal gas remains constant. This means heat supplied to the system is used to do work against the surroundings. When a solid melt into liquid, its internal energy increases.

Q.5. Who is the father of thermodynamics?
Ans: Nicolas Léonard Sadi Carnot is often described as the “Father of Thermodynamics.”

Q.6. Who wrote the law of thermodynamics?
Ans: By \(1860,\) as formalized in the works of scientists such as Rudolf Clausius and William Thomson, what are now known as the first and second laws were established. Later, Nernst’s theorem (or Nernst’s postulate), which is now known as the third law, was formulated by Walther Nernst over \(1906 – 12.\)

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