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Calculating Enthalpy in Thermodynamic Units

Key Takeaways

  •  Enthalpy is a measure of the total energy content within a thermodynamic system.

  • According to Hess’s law,  the total enthalpy change is the sum of individual enthalpy changes when the reaction is broken down into multiple steps.

  • When a single reaction involves different temperatures, Kirchhoff’s law facilitates enthalpy change calculations in relation to heat capacity. 

The value of enthalpy reflects the capability of a thermodynamic or steady flow system to release heat and perform work. This involves the process of heat absorption or release during a reaction, which is the enthalpy change. The enthalpy change of a reaction highly influences the reaction types (endothermic, exothermic), phase transition (solid-liquid-gas), and other thermal phenomena. This also means the involvement of different types of enthalpy changes, such as the enthalpy of combustion, formation, or neutralization.

Working out the total enthalpy change through these different routes is an important part of the thermodynamic flow design cycle. In this article, we will address the ways of calculating enthalpy change by implementing theories like Hess’s law. 

Enthalpy and Enthalpy Change Calculations

Enthalpy is the total energy content in a thermodynamic system and can be calculated numerically as the sum of internal energy and the product of pressure and volume of the system. 


The term pV is the amount of work done by the system. For instance, if flow in a fluid system is considered, the work is done to drive the flow in or push it out of the device, such as a pump.      

There are various unknown or insignificant factors involved in the measurement of enthalpy, so instead of calculating enthalpy itself, we simplify the calculation by calculating the change in enthalpy. Mathematically, it can be expressed as:

ΔH= ΔU + pΔV

Where Δ represents the change, H is enthalpy, U is internal energy, p is pressure, and V is the volume of the system.

The above equation is true only when the work is performed at constant pressure. However, this also means that the change in enthalpy is equal to the heat absorbed or released in the system, according to the first law of thermodynamics:

ΔH= Δq

This equation is important in identifying what type of reaction occurs within the system. 

  • When q is positive, endothermic reaction—heat is absorbed  

  • When q is negative, exothermic reaction—heat is released

Hess’s Law

 Understanding Hess’s law

An ideal way to approach the enthalpy change calculation is with Hess’s law, which states that the total enthalpy change of a reaction can be the sum of each individual enthalpy when the reaction is broken down into two or more steps. We know the expression for enthalpy of formation is: 

Enthalpy of formation

For instance, let's take a look at the following reaction,

CS2+3O2 CO2+2SO2

In this reaction, we can break down the reactions for CS2, CO2, and 2SO2 and calculate their individual enthalpy change to sum up the total enthalpy change. It is, however, important to note that in order for Hess’s law to be valid, all the individual reactions should occur at the same temperature.

Enthalpy Change Due to a Variation in Temperature

Not all steps of a reaction can occur at the same temperature. Kirchhoff’s law of thermochemistry provides a way of addressing this dissimilarity and calculating enthalpy change with relation to the heat capacity of the products and reactants. This can be expressed as:

 Kirchhoff’s law for calculating enthalpy variation

Integrating this equation we get, 

Here, Cp is the heat capacity, which defines the amount of heat required by the material to raise its temperature by a unit. 

This equation enables an understanding of the temperature dependency of the reaction. When the temperature increases or decreases due to the heat flow, calculating enthalpy changes help us understand the nature of the reaction. 

Calculating Enthalpy for Thermodynamic Simulations With CFD

In the design of any system concerning mass and heat transfer, calculating enthalpy is an important step. It enables the analysis of heat content, which facilitates the derivation of important work from the system. Different chemical reactions occur within this system, the nature of which can be analyzed with enthalpy change along with the understanding of heat gained or lost. This analysis requires solving energy equations and relevant enthalpy changes as well as their accurate representation in a simulation model.

Advanced CFD tools like Omnis can facilitate this by running high-fidelity numerical simulations. By calculating enthalpy changes, the internal and external work required across the control volume as well as a power requirement evaluation can be done for a wide range of flow and boundary conditions.

Subscribe to our newsletter for the latest CFD updates or browse Cadence’s suite of CFD software, including Omnis and Pointwise, to learn more about how Cadence has the solution for you. 

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About the Author

With an industry-leading meshing approach and a robust host of solver and post-processing capabilities, Cadence Fidelity provides a comprehensive Computational Fluid Dynamics (CFD) workflow for applications including propulsion, aerodynamics, hydrodynamics, and combustion.

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