# Enthalpy change vs. change in internal energy in a system

I've been trying to get my head around the differences between enthalpy change and internal energy change for a system. Here's my understanding of it so far. I'd appreciate any feedback on my understanding so far on the concepts - especially if there are misconceptions (and there probably are)

• Internal energy is the 'intrinsic' energy of some system, can be measured with reference to something within the system, e.g. chemical bonds, vibrational energy states, etc.
• Enthalpy change is the heat (i.e. energy transferred due to temperature difference) change at constant pressure due to some chemical process.

$\Delta H = \Delta U + P \Delta V$

$\Delta H$ is characteristic of a given chemical process - i.e. this value is the same regardless of what conditions it is run under (e.g. varying pressures, volumes, starting temperatures). As long as it's the same reaction, $\Delta H$ will be the same. It's the overall energy input required to make a process work, and is split between influencing $U$ and performing $PV$ work.

$\Delta U$ is a function of the specific conditions (i.e. volume, pressure) in which a specific instance of a chemical process is run.

So it's theoretically possible to set up a chemical process (say vaporisation) to run in such a way so that $\Delta U$ is zero, and all the enthalpy change is accounted for in the $P\Delta V$ term?

And what about cases where P is not constant? What happens then? Can we calculate the value of $\Delta H$? And does $\Delta H$ even have a meaning in this case?

Both $$U$$ and $$H$$ are not directly related to any particular process. They are physical properties of the material being processed, and are unique functions of the thermodynamic state of the material, and not the process. They are directly proportional to the amount of material, and its thermodynamic state is characterized by its temperature and pressure (and composition for a multicomponent system). The internal energy is a fundamental property, but the enthalpy is a defined property given by $$H = U + PV$$, and is just a convenient parameter to work with is solving many kinds of thermodynamics problems.
For a process carried out at constant pressure in a closed system, the amount of heat $$Q$$ added to the system turns out to be equal to the change in enthalpy between the initial state of the material and the final state of the material. For a chemical reaction carried out at constant pressure, the amount of heat $$Q$$ that must be added to the system in order for the final temperature of the products to equal the initial temperature of the reactants turns out to be equal to the enthalpy of the pure products minus the enthalpy of the pure reactants at that temperature. Both these results follow from the first law of thermdynamics.
And what about cases where $$P$$ is not constant? What happens then? Can we calculate the value of $$ΔH$$? And does $$ΔH$$ even have a meaning in this case?
Since $$H$$ is just defined as $$U + PV$$, we can always calculate the change in enthalpy between two thermodynamic equilibrium states of a system. $$\Delta H$$ certainly has a value in this case, even if it is not equal to the amount of heat added for a process between the two states.
The critical thing to remember is that $$U$$ and $$H$$ are physical properties of the materials comprising a system, and are independent of any specific process.