What is the difference between \(\Delta H\) and \(\Delta E ?\)

Enthalpy (H) is a thermodynamic property that represents the total energy of a system, including both its internal energy (E) and the energy related to its pressure and volume. It is defined as: \(H = E + PV\) Where, \(H\) is enthalpy, \(E\) is internal energy, \(P\) is pressure, and \(V\) is volume. Internal Energy (E) is the total energy stored in a system, including kinetic energy, potential energy and other forms of energy (including molecular bonds, electron configuration, etc.).

The change in enthalpy (\(\Delta H\)) represents the difference in the enthalpy of a system before and after a process or reaction has taken place. Similarly, the change in internal energy (\(\Delta E\)) represents the difference in the internal energy of a system before and after a process or reaction has occurred. Mathematically, these changes are represented as: \(\Delta H = H_{final} - H_{initial}\) \(\Delta E = E_{final} - E_{initial}\)

From the definition of enthalpy, we know that: \(H = E + PV\) Taking the change in enthalpy and change in internal energy, we can write: \(\Delta H = \Delta E + \Delta (PV)\) This equation shows that the difference between the changes in enthalpy (\(\Delta H\)) and internal energy (\(\Delta E\)) depends on the change in the product of pressure and volume during a process or reaction. In some cases, \(\Delta H\) and \(\Delta E\) may be equal or approximately equal, such as when the process or reaction occurs under constant volume or constant pressure conditions, and the system does not perform any work. In general, the difference between the two depends on the specific conditions of the process or reaction.