Enthalpy and entropy are terms commonly encountered in the field of thermodynamics.
In a very simplified model of explanation, both the terms enthalpy and entropy are measure of energy.
Before I continue with explaining each of them, I feel it is necessary for me to introduce some concepts of thermodynamics.
The first Law of thermodynamics- Energy is conserved.
This is an essential law, for calculations involving energy to be possible. If we were to define a closed boundary (more comprehensive if I say “control volume”) with absolute insulation from the environment, energy within this system is constant. It can also be said that the internal energy of the system is constant.
This internal energy, commonly denoted by U in thermodynamic context, can be increased or decreased when there is a source of energy supplied to it. Such sources of energy can come from a change in gravitational elevation, a change in system pressure, heat added to the system, and etc.
When we consider energy, it is reasonable to use the concept of enthalpy, which is essentially has the same meaning as internal energy, subjected to isobaric (constant pressure) conditions. It is used more often because what we encounter is usually subjected to the constant atmospheric pressure.
In thermodynamics enthalpy is denoted by H, and H = U + pV, whereby p is the system pressure and V is the system volume. Imagine a balloon filled with water and boils on its own (without heating). This balloon (assuming it doesn’t burst) will increase in volume due to larger volume occupied by gaseous water vapour. To increase the volume, the contents in the balloon have to overcome the pressure exerted on it by the atmosphere. Hence the pV term.
But generally, enthalpy has no appreciable meaning unless we measure the change in enthalpy. Suppose now, the water boils in the same balloon with a heater heating the water, there obviously is a change in the internal energy U (as heat energy is supplied). And the change in enthalpy of the system is the amount of heat supplied to heat the water.
In Chemistry, the enthalpy of a reaction (to determine endothermic or exothermic) is determined by measuring the temperature of the starting mixture and the temperature of the ending mixture, assuming no change in pressure and volume, the pV term is ignored. Using the final and initial temperatures, as well as the (usually average) heat capacity of the mix, the enthalpy may be calculated.
So, if we can program a computer with suitable inputs, i.e. the average heat capacity of the mix, the computer can monitor the temperature of the reaction to give us an enthalpy change profile.
Hence enthalpy is something measureable, a form of usable energy.
Having a very simple idea on the concept of enthalpy, I shall now discuss entropy (denoted by S in thermodynamics), a more abstract term encountered in thermodynamics. In contrast to enthalpy, it is actually a non-working energy.
What do I mean by non-working? Entropy is actually a measure of randomness, and overall entropy is said to be ever increasing. When a process occurs, overall entropy stays constant or increase, but never decrease.
For example, at a molecular scale, the freezing of ice in a refrigerator: entropy (randomness) is decreased when the water molecules pack together neatly as the heat is removed from the water. At the same time, the heat is absorbed by the coolant and then reject to the external environment, which rises the temperature of air near the heat dissipating fins, this make the air molecules collide with one another more often, increasing entropy. This process is working against the law of heat going from a region of higher temperature to a region of lower temperature, so we can expect more energy input is required in freezing than melting, as such, more heat is dissipated. So the overall entropy here is increased. Applying similar reasoning on melting of ice, since we are not going against any law of nature, we at most can only expect the overall (total) entropy to be constant.
It is a term introduced to explain the phenomenon of kinetic or electrical energies may be efficiently converted to heat, but the conversion of heat to other useful energies are always inefficient. This is due to the non-working energy involved to work against the law of nature.
So in a nutshell, besides the difference in notation in thermodynamics (H and S), enthalpy is a measure of working energy and entropy is a measure of non-working energy.