# Internal Energy and Enthalpy in Thermodynamics

### Key Takeaways

• Enthalpy is a measure of the total heat energy, absorbed or released, in a thermodynamic system.

• Internal energy indicates the total energy, potential or kinetic, in a thermodynamic system.

• The relation between internal energy and enthalpy in thermodynamics can be established by calculating the changes or studying the temperature relations.

# The general law of thermodynamics deals with quantities like temperature, heat, work, internal energy, and their relation. These relations often establish the interlink between the science of thermodynamics and fluid dynamics, where concepts such as fluid flow and heat transfer can be utilized to perform the work within a system. An example where this can be observed thoroughly is in engines or heat transfer machines where working fluid can drive the thermodynamic cycle.

The enthalpy in a thermodynamic system is an important variable that defines the total heat associated with a system. The analysis of the enthalpy change and internal energy change during a reaction is an important guide to maintaining efficiency in thermodynamic engineering.

## Discussing Change of Enthalpy in Thermodynamics

Enthalpy is the total heat absorbed or released in a thermodynamic system. Mathematically, it is often described as the sum of the internal energy and the work performed:

H= U+pV

H is the enthalpy, U is the internal energy, p is the pressure, and V is the volume of the fluid system. The product of pressure and volume is the work performed. Generally, the enthalpy change in the system is the desired calculation, as it simplifies the energy transfer analysis. As such, the above equation can be written as:

ΔH= ΔU+pΔV

For the above equation to be true, the pressure must be constant. The equation can indicate the nature of the reaction, i.e., whether it is endothermic or exothermic. The positive enthalpy change means the reaction is endothermic, where the system absorbs the energy. The negative value of enthalpy change means the reaction in the system is exothermic, where the heat is released during the process. At the zero value of enthalpy change, the thermodynamic reaction is considered to be in equilibrium.

Given that both the internal energy and the enthalpy in a thermodynamic system describe the energy associated with the system, it is important to establish the differentiation between the both. The internal energy is the heat energy of the system at constant volume while the enthalpy is the heat energy under constant pressure. We will discuss the internal energy in thermodynamics next.

## Relation With Internal Energy

Internal energy signifies the total energy, kinetic and potential, of a thermodynamic system. From the above equations, we know that enthalpy and internal energy are directly influenced by each other. However, understanding the absolute value of internal energy in a system is difficult given the uncertainty of internal energy components. Thus, the change in internal energy is calculated, which is also an important factor in determining enthalpy change.

For a closed system, the first law of thermodynamics holds true, according to which the total energy remains constant. This can be expressed as:

ΔU=δQ-δW

Q is the heat energy supplied to the system and W is the work done.

The relation between enthalpy and internal energy can also be established by studying temperature relations. According to the second law of thermodynamics, for absolute temperature T and entropy S:

δQ=TdS

The above equation for change in internal energy can be written as:

dU=T dS - p dV

This can be further simplified to get:

dH=TdS+Vdp

The increase in temperature of the system induces kinetic energy, which changes the internal energy of the system. This also influences the enthalpy change within the thermodynamic system.

## Calculating Thermodynamic Variables With CFD

When the fluid and its thermodynamic properties are the driving factors of energy transfer in a system, the calculations of variables like enthalpy, internal energy, and temperature become critical. The enthalpy equation establishes the understanding of heat transfer and power requirements for the system to operate. The numerical solution for temperature requirements can be determined for the enthalpy and internal energy changes to occur. In the case of compressible flow, pressure and power requirements can be calculated from the enthalpy equation. The calculation can be complex for incompressible flow given the challenge to establish the relationship between temperature, pressure, and density of the working fluid. In such a case, the Navier-Stokes and continuity equation can be applied.

Solving the various equations associated with a thermodynamic system can be done using CFD simulation packages. By running high-fidelity simulations, the changes in internal energy and enthalpy in a thermodynamic system can be analyzed accurately, which is critical to understanding the heat transfer within a system. By generating a heat transfer model, running a thermodynamic system simulation, and solving the governing equation for different pressure, volume, and force conditions, efficient thermodynamic design can be achieved.