# Considering enthalpy of formation and sensible enthalpy in steady-flow systems

I am reading a book (Thermodynamics an Engineering approach), I am reading over the section of steady-flow systems with chemical reactions.

The book just introduced the following formula for the enthalpy (per mole) of a component as:

$$\bar{H} = \bar{h_f^o} + (\bar{h} - \bar{h^o})$$

Where $$\bar{h_f^o}$$ is the standard enthalpy of formation at the reference state of 25 ºC and 1 atm, and $$\bar{h^o}$$ is the sensible enthalpy at the standard reference state of 25 ºC and 1 atm.

How are these two quantities different? In my book they give an example where they calculate the enthalpy for oxygen at 7 ºC, they express it as:

$$\bar{H}_{O_2, @7 ºC} = (0 +\bar{h}_{280K} - \bar{h}_{298K} )$$

where $$\bar{h}_{280K}$$ = 8150 kJ/kmol

and $$\bar{h}_{298K}$$ = 8669 kJ/mol

Considering the work done by a turbine as $$W = \dot{m}(h_{10kPa}-h_{5kPa})$$ I'd normally take the enthalpy values given by a pressure table and use that directly. I can see that using $$\bar{H}$$ the term, $$\bar{h_f^o}$$, will cancel out if there are no chemical changes in the system. I do not quite get how this enthalpies values relate-to or differ from the ones that are listed in pressure or temperature tables.

• Can you short out the chemistry equation arrow in: $\ce{1 kmol O_2 \cdot (0 +\bar{h}_{280K} - \bar{h}_{298K} ) }$ ? Commented Jul 31 at 16:22

In your first equation, the difference in parentheses is the sensible enthalpy change, that is due to temperature only (for ideal gas enthalpy is function of temperature only). The first $$h_f$$ with circle is the standard enthalpy of formation which is zero for an element in the most common state (so for O2 it is zero). The values you quote use a different zero for enthalpy (probably 0 at 0 K).
• Thank you very much for your response, really appreciate it. I was also wondering, if the listed $h$ values in the tables correspond to $h$ in $h_f + h - h_0$ or would they correspond to just $h$?
• The author uses $h^o$ (the last h in equation) for enthalpy at his reference point (25 C). The first $h$ is for standard enthalpy of formation. For combustion of say methane with oxygen to yield carbon dioxide, the standard heat of formation of each allows you to calculate the heat release. Commented Aug 2 at 19:31