What is the use of enthalpy? Just like the internal energy, only change in enthalpy is physically useful concept. From the definition of the enthaply, \(H = U + pV\text{,}\) we find that the change in enthalpy for an infinitesimal process will be the difference,
\begin{equation*}
(H+dH) - H =\left[(U+dU) +(p+dp)(V+dV \right] - (U+pV)
\end{equation*}
Expanding and dropping quadratic terms in infinitesimals, we find the following.
\begin{equation*}
dH = dU + p dV + V dp
\end{equation*}
Now, from the first law of thermodynamics, we have \(dU = dQ - pdV\text{.}\) Therefore, for \(dH\) we will have
\begin{equation}
dH = dQ + Vdp.\tag{24.25}
\end{equation}
If a process occured under constant pressure conditions, then the second term will be zero. Thus, for any process in which pressure is maintained at some value, say at atmospheric pressure, the change in enthaly \(\Delta H\) will equal heat \(Q\) into-the-system. This is why enthaly is sometimes called the heat function.
\begin{equation}
\Delta H = Q.\ \ \ \text{(Constant Pressure Process)}\tag{24.26}
\end{equation}
This is reminiscent of constant-volume processes, in which first law of thermodynamics say that change in the internal energy will equal heat into-the-system.
\begin{equation}
\Delta U = Q.\ \ \ \text{(Constant Volume Process)}\tag{24.27}
\end{equation}
Many engineering processes and chemical reactions are conducted at constant pressures. For these systems enthalpy is a more appropriate quantity for analysis. For instance, if a chemical reaction that releases \(10\) kJ of energy takes place at atmospheric pressure, we say that the enthalpy of the products is less than those of the reactants by \(10\) kJ. The latent heat is another example of enthalpy since latent heat is usually measured at atmospheric pressure.
Some experiments such as heating or cooling of solids or gas in a rigid container are often accompanied by very little change in volume. In those situations, we will prefer using internal energy since heat-into-the-system equals change in internal energy.
Clearly, we can write Eqs.
(24.26) and
(24.27) in terms of specific heat or heat of transformation, whichever is applicable to the heat process.
\begin{align}
\amp dH = m\, c_p,\ dT \ \ \text{or}\ \ \ l\, dm\tag{24.28}\\
\amp dU = m\, c_V,\ dT \ \ \text{or}\ \ \ l\, dm\tag{24.29}
\end{align}
