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Enthalpy Definition and Derivation

What is Enthalpy?

Enthalpy is defined as the amount of internal energy and the output of a thermodynamic system's pressure and volume. Enthalpy is an energy-like property or state function that has energy dimensions (and is thus calculated in joules or erg units). The enthalpy H is equivalent to the sum of the internal energy E and the pressure P multiplied with volume V of the system i.e., H = E + PV, respectively.


Under the law of conservation of energy, the shift in internal energy is equal to the heat transmitted to the device, minus the work performed by it. If a change in volume at constant pressure is the only work performed, the change in enthalpy is exactly equal to the heat transferred to the device. The amount of energy is called the enthalpy (or latent heat of vaporization) and is expressed in units of joules per mole when energy needs to be applied to a substance to shift its phase from a liquid to a gas.


Enthalpy Change

The name given to the amount of heat evolved or consumed in a reaction conducted at constant pressure is Enthalpy transition. The symbol of Enthalpy H is referred to as "delta H". At constant pressure, the equation for the change in internal energy, ∆U = q + w can be written as:

∆U = qP – p∆V

Where qP represents the heat absorbed by the system at constant pressure and – p∆V is the expansion work done due to the heat absorbed by the system. The above equation can be written in the terms of initial and final states of the system which is defined below:

UF – UI = qP –p(VF – VI)

Or qP = (UF + pVF) – (UI + pVI)

Enthalpy (H) can be written as H= U + PV. Putting the value in the above equation, we obtained: 

qP = HF – HI = ∆H

Hence, change in enthalpy ∆H = qP, referred to as the heat consumed at a constant pressure by the system. At constant pressure, we can also write,

∆H = ∆U + p∆V


Some Key Points

The heat from the device is lost to the surrounding atmosphere during exothermic reactions. ∆H is negative for such reactions. During endothermic reactions, heat is absorbed from the atmosphere by the system. ∆H is positive for such reactions.


Enthalpy of Reactions: 

Energy change (U) is equal to the amount of heat produced and the work carried out. Pressure-volume work is called work performed by an expanding gas (or just PV work). For instance, consider a gas-producing reaction, such as dissolving a piece of copper in concentrated nitric acid. 

Cu(s)+ 4HNO3(aq) → Cu(NO3)2 (aq) + 2H2O(l) +  2NO2(g)

The quantity of PV work performed by multiplying the external pressure P by the volume change induced by the piston movement (almost V) is found. At constant external pressure, (here, atmospheric pressure),

W = −PΔV

The negative sign associated with PV work performed means that when the volume increases, the device loses energy. The work performed by the system is negative if the volume increases at constant pressure (V> 0), implying that a system has lost energy by performing work on its surroundings. Conversely, the work performed by the system is positive if the volume decreases (almost V<0), which implies that the environment has worked on the system, thereby increasing its energy.


The internal energy U of a system is the sum of all its components' kinetic energy and potential energy. It is the inner energy shift that generates heat plus function. Chemists typically use a related thermodynamic quantity called enthalpy (H) to calculate the energy changes that occur in chemical reactions. Systems’ enthalpy is defined as the sum of their internal energy U plus the product of their pressure P and volume V:

H=U+PV


Since all state functions are internal energy, strain and volume, enthalpy is also a state function. We can therefore characterize a shift in enthalpy ('H) accordingly.

ΔH=Hfinal −Hinitial

If at constant pressure (i.e. for a given P, ΔP=0) a chemical shift occurs, the change in enthalpy ( ΔH) is 

ΔH=Δ(U+PV)

=ΔU + ΔPV

=ΔU + PΔV

Substituting q+w for ΔU (First Law of Thermodynamics) and −w for PΔV we obtain    

ΔH=ΔU+PΔV

 =qp+w−w

 =qp

The p subscript is used here to emphasize that this equation is only valid for a constant pressure phase. It is observed that the shift in enthalpy, the H of the system, is equal to the heat obtained or lost at constant pressure.

ΔH=Hfinal−Hinitial

 =q


System in Thermodynamics

A thermodynamic system is a part of matter with a defined boundary on which we concentrate our attention. The system boundary might be fixed or flexible, and it can be real or fictitious. The 3 types of systems in Thermodynamics are-

  • Isolated System - A system that is separated from its surroundings is unable to exchange both energy and mass. The cosmos is thought to be a self-contained system.

  • Open System - Both mass and energy can be moved between the system and its surroundings in an open system. 

  • Closed System - The transmission of energy happens across the closed system's border, but the transfer of mass does not. 


Different Branches of Thermodynamics

Thermodynamics has 4 major branches, they are

  • Classical Thermodynamics - The behaviour of matter is investigated using a macroscopic approach in Classical Thermodynamics. Individuals consider units such as temperature and pressure, which aids in the calculation of other properties and the prediction of the characteristics of the matter conducting the process.

  • Statistical Thermodynamics - Every molecule is in the limelight in Statistical Thermodynamics, which means that the properties of each molecule and how they interact are taken into account to characterise the behaviour of a group of molecules.

  • Chemical Thermodynamics - The study of how heat & work interacts with each other in a given chemical reactions and state transitions is known as Chemical Thermodynamics.

  • Equilibrium Thermodynamics - Equilibrium Thermodynamics refers to study of energy & matter transitions as they approach towards equilibrium.


Tips to study Thermodynamics

Thermodynamics is one of the most important chapters in chemistry as aspects of it (Carnot Engine), also appears again in Physics in later chapters.


Thermodynamics also has a lot of weightage in competitive exams like JEE, etc.  To get good marks in Thermodynamics, the fundamentals of the chapter, i.e. understanding of different types of systems and energy, etc must be crucial as it sets the base for the complex topic that builds on it. The students should start by going through the NCERT chapter once or twice and then solve all the NCERT Exercises. They can find solutions to these Exercises at Vedantu's official website. If the student has some doubts or needs revision of any topic of Thermodynamics, they can check out Vdantu's Youtube Channel. Here they can find several video lectures on Thermodynamics and other topics. 


Teachers also conduct live sessions where questions and solutions are discussed to help the students who don't have the best means to a teacher. Solving questions is really important for understanding Thermodynamics as it has many concepts which relate to formulas and conditions. Students can find the list of important questions of thermodynamics and other topics at Vedantu;'s official website. Previous year's questions are also one of the most suggested ways to study and prepare for exams as it helps to break down the questioning pattern and help the student to explore different types of questions. 


This also helps them to create an exam-like situation that gives them a real test with time limits. They can find the papers and solutions at Vedantu's official website. Students should definitely utilize these FREE resources to clear their concepts and their way to get good marks. Vedantu is trying to bring the best out of every child who wants to achieve something or has a zeal to do hard work. A little hard work with some guidance can help any child to achieve the sky and make their parents and teachers proud. 

FAQs on Enthalpy Definition and Derivation

1. Is Enthalpy Positive or Negative?

In an exothermic reaction, the change in enthalpy is negative as the total heat is lost ("Exo-Thermic” means that heat is leaving). If H is negative, which is the total decrease in enthalpy achieved by heat generation, a favourable change in enthalpy during an endothermic reaction will be the reverse of this. The reaction is endothermic if ΔH is positive; that is, heat is absorbed by the system due to a greater enthalpy of the reaction products than the reactants. To break a bond, a positive change in enthalpy is required, while the forming of a bond is followed by a negative change in enthalpy.

2. What is the Significance of Enthalpy?

The thermodynamic system enthalpy, denoted by H, can be calculated using the following equation: 

H = U + PV 

Where the inner energy of the system is U, the pressure is P and the volume is V. The entropy of an isolated system can never decrease as per the second law of thermodynamics, i.e. the entropy change of an isolated system can only be positive or zero. Therefore, only when the shift in the entropy of the universe is positive can a mechanism be feasible. This means that any approach which does not violate the second thermodynamic law must increase the entropy of the universe.

3. What is Thermodynamics?

Thermodynamics is the branch that deals with the movement of energy from 1 form to another. Thermodynamics is the connection between heat and temperature with energy and work done. The chemical reactions which release heat energy are transformed into different usable forms established on the laws of thermodynamics. Energy can only be transformed from 1 form to another form used in different industries. Thermodynamics consists of 3 laws that govern it. Students can learn more about the laws of Thermodynamics at Vedantu's Website or Youtube Channel.

4. What are 3 laws of Thermodynamics

The 3 Laws of Thermodynamics are-

  • The 1st law is also called The Law of Conservation of Energy. The first law of thermodynamics explains that any form of energy can never be created or get destroyed in an isolated system. 

  • The 2nd law of thermodynamics explains that the entropy of any isolated system always keeps on increasing.

  • The 3rd law of thermodynamics says that the entropy of a system reaches to a constant value as the temperature reaches absolute 0.

5. What is the Carnot Cycle?

Carnot’s Cycle is an ideal cycle that leads to the second law of thermodynamics. It was first invented in 1824 by a French physicist, Sadi Carnot. To achieve a point of steady supply of work, the working substance is subjected to a cycle of quasi-static operations called Carnot’ cycle. The cycle acts as a heat engine. The Carnot’s heat engine is completely reversible which means that it can be used in the reverse direction too. The Carnot’s heat engine, the process of isothermal and adiabatic expansions, and compressions are carried out quasi-static which is an ideal case. No engine can practically fulfill these conditions.

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