Enthalpy - Definition and Derivation

Energy can neither be created nor be destroyed. It can only be transformed into various forms which are interchangeable. For instance, tides are harnessed to convert tidal energy into electrical energy. Similarly, we rotate a turbine to convert the mechanical energy into electrical energy. Also, this electrical energy is further converted into light or heat energy by lighting a bulb or an appliance. 

Simultaneously, enthalpy is one such term that describes the amount of change in energy during the process of conversion. Students have to understand enthalpy definition and derivation for a comprehensive study of the same. Therefore, to make it easier and more straightforward, here is a brief explanation along with relevant diagrams and examples along with mathematical equations. 

Enthalpy - Definition 

Enthalpy is the quantity of heat in a system. This heat is utilised in the occurrence of a process. Any heat-related system is called a thermodynamic system, so enthalpy is a thermodynamic quantity.

Besides, it should be noted that any system comprises of multiple participants. Each of these participants has its pressure and volume. As we already know, the product of pressure and volume of a specific system is constant. 

This enthalpy is equal to the sum of internal energy of such a system with the constant. 

You need to understand that the forms of energy get changed, but enthalpy remains constant. For example, when water freezes into ice, some amount of energy is spent in doing the work, which is called enthalpy.

As a result, scientists are often found to be calculating enthalpy instead of energy. You should be cautious about learning both the terms. Although they seem to be equal, they are actually not. 

Enthalpy - Mathematical Equation

Similar to any other scientific theory, enthalpy also has a mathematical formula. Refer to the image below. It shows the equation of enthalpy definition and derivation with appropriate labels.

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You should note that Δ (delta) is a symbol that represents a change in some quantity. Herein the change in internal energy is expressed through ΔU. 

Also, consider another essential aspect; that of energy loss due to it being is used up for work. This amount of energy shall be deducted from the amount of heat added to the system to find the actual amount of energy change.

These are basic terms and expressions, which will help in understanding the overall concept with clarity. 

It is often observed that students confuse both these terms - entropy and enthalpy. Also, they often use it interchangeably. However, the ground reality is entirely different. Both these terms are hugely different. 

Refer to the table below for a clear comparison -

Enthalpy and Entropy

Sl. No. 




It is a property that helps in the measurement of the movement of molecules.

It is a type of energy that is composed of both internal energy and energy flow.


It is considered only under limitations or controlled conditions.

It can be measured or is applicable at normal or regular conditions.


The unit of measurement is Joule per Kelvin.

The measuring unit is Joule per mole.


A thermodynamic system is likely to favour a maximum amount of entropy in it.

Any thermodynamic system will favour only a minimum amount of enthalpy.

Now, that you know the difference, it is quite clear that enthalpy definition and derivation is a form of energy. So, when the internal energy changes, it is called enthalpy during constant pressure.

As mentioned above, there are other properties, such as pressure and volume. Let us dig deeper into those terminologies to understand enthalpy. 

 Enthalpy - Relation with Volume and Pressure

Herein, let us consider a situation where there is no work done. In terms of Chemistry, we are considering a chemical reaction as a system which is capable of performing a certain action. However, for the sake of understanding, we are acknowledging that no work is being done.

Hence, if any amount of energy is emitted or absorbed from or by the system, there would be an equal amount of change in internal energy. It is observed that this kind of reaction is possible only when the volume and pressure are constant. 

Nevertheless, the experiments are conducted in open flasks, resulting in exchange of heat within and outside the surrounding. This further leads to the concept of work done and enthalpy.

You should note that work done implies both ways; it is not just surrounding works on the system or vice versa.  Since a specific amount of energy has been spent on doing work, the heat absorbed or emitted is not equal to internal energy.

Thus, internal energy equals the sum of work done and the product of volume and pressure. The enthalpy definition and derivation is represented as -

H =  E + PV

Where H = enthalpy

E = internal energy

P = pressure 

V = volume

Therefore, now if we want to represent the changes in energy levels or enthalpy, we can write it as -

ΔH =  ΔE + Δ(PV)

With this, you should note the following two points -

  • At constant volume, the heat emitted or absorbed during a reaction equals the internal energy of a system.

  • At constant pressure, heat emitted or absorbed during a chemical reaction equals the enthalpy of the system.

Both these points again go back to the original equation. Make sure you understand the individual concepts so that you can follow the comparison well. 

Preparing for a subject requires you to be clear on every topic included in it. You should be able to relate enthalpy definition and derivation with the subject matter at hand. Being familiar with the concepts and numerical in that specific chapter is the key to ace the exam.

Endothermic and Exothermic Reactions

If you look carefully at both the terms, you can decipher their meanings. Thermic means heat. Similarly, ‘exo’ means outside, and ‘endo’ refers to inside. Therefore, when a system pulls in heat from the outside surrounding, it is termed an endothermic reaction. 

On the other hand, if a system gives out heat into the surrounding, it is called an exothermic reaction. Now you can understand that it is neither hot, nor cold. It is only the absence of heat that defines coldness. 

Similarly, when there is a presence of heat, an object is said to be hot. So, when heat leaves an object, that specific place becomes cold as a fall in temperature. Now, the takeaway points in this regard are as follows -

  • Endothermic reactions contain more energy within them, whereas exothermic reactions do not have much energy within them.

  • Endothermic reactions make their surrounding cooler, but exothermic reactions make their surroundings hotter.

Now that you have developed an idea over the enthalpy definition and derivation, it is time that you test your understanding. Below is an exercise for you to check your learning.

Test Your Understanding

Fill in the blanks

  1. During constant volume, change in internal energy is equal to ………..heat.

  2. Enthalpy is an ……………...property of a system.

  3. …………...of an ideal gas depends on the temperature.

  4. Heat  …………..at constant …………, increases the enthalpy of a system.

  5. Enthalpy and internal energy are propertied of the temperature of an ……..gas.

  6. Heat is supplied at constant pressure, there is a change in ………..

  7. Enthalpy changes can be found using ………, which cannot be found by a calorimeter.

  8. Endothermic changes are represented by………. values.

  9. Which of the following reaction is endothermic?

  1. Melting copper

  2. Melting ice

  3. Freezing water

  4. Butane combustion

  1. When enthalpy of a substance directly changes from a solid to vapour, it is called ……….

  2. Which is an intensive property?

  1. Temperature

  2. Viscosity

  3. Surface tension

  4. All of these.

  1. There is a ……….. in temperature in case of adiabatic expansion.

  2. During the formation of a chemical bond, ……….is released. 

Answers: transferred, intensive, enthalpy, transferred, pressure, ideal, enthalpy, Hess’s law, positive, melting copper, all of these, decrease, energy

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FAQ (Frequently Asked Questions)

1. What is enthalpy?

Ans. Enthalpy is the amount of heat absorbed or emitted by a substance during a change at constant pressure.

2. How are enthalpy and energy not the same?

Ans. Energy and enthalpy are not the same, since the latter is the amount of heat released or absorbed during a change. Here, energy is the overall kinetic and potential energy in a system.

3. What property does enthalpy display, extensive or intensive?

Ans. Enthalpy is an extensive property. The value of enthalpy depends on the mass of a substance.

4. Why is enthalpy necessary?

Ans. Enthalpy is vital in calculating the amount of heat exchange during a change in a substance. It helps in assessing if the reaction was endothermic or exothermic.