It is not immediately obvious how one would define the total amount of energy in a system. This is because depending processes used to extract energy, different amounts of energy may be extracted. Consider a system of hot gas. We may, for example, cool the system to absolute zero, removing energy by heat transfer, while keeping the volume constant. Alternatively, we may cool the gas to absolute zero, removing energy by heat transfer, while keeping the pressure constant. These two methods extract different amounts of energy by heat transfer, and so correspond to different concepts of extractable energy.
Internal energy is the proper metric which is conserved in all cases, its change being equivalent to heat transfer minus work. In principle, the specific internal energy is the sum of all kinetic and potential energies per unit mass. Conceptually, consider the potential energy created by intermolecular forces and the molecular-scale vibrational kinetic energy of temperature.
$$ \Delta U=Q-W $$
However, when applied to simple compressible systems, internal energy ****will be particularly useful for determining heat transfer directly for constant volume processes, whereas a modified metric, enthalpy, will be useful for determining heat transfer directly for constant pressure processes
The internal energy of a system indicates how much heat can be extracted by constant volume processes. The change in internal energy of a constant volume process is therefore equivalent to the heat transfer of the process.
$$ m(\Delta u)=Q_{v=c} $$
Since work may be calculated by the integral of pressure with respect to volume, the work for a constant volume process always goes to zero. This is why internal energy may be used to determine the heat transfer of constant volume processes directly.
$$ \Delta U=Q-W=Q-\int pdV\Rarr\Delta U=Q_{v=c} $$
The enthalpy of a system indicates how much energy can be extracted by constant pressure processes. The change in enthalpy of a constant pressure process is defined such that it is equivalent to the heat transfer of the process.
$$ m(\Delta h)=Q_{p=c} $$
Specific enthalpy is defined as the specific internal energy plus the product of the substance’s pressure and specific volume. This definition works for determining the heat transfer of constant pressure processes because enthalpy’s $pV$ term and the work term entailed by the internal energy cancel out in the conservation of energy.
$$ h=u+pv $$
$$ \Delta H=\Delta U+\Delta (pV)=Q-W+\Delta (pV)=Q-\int pdV+\Delta (pV)\Rarr\\\Delta H=Q_{p-c} $$
Note that enthalpy is not properly conserved, rather internal energy is truly conserved, but by using enthalpy we account for and therefore may otherwise neglect the work involved in constant pressure processes.