The Laws of Thermodynamics, Entropy, and Gibbs Free Energy

professor Dave here, let's learn the laws of thermodynamics the laws of thermodynamics help us understand why energy flows in certain directions and in certain ways. a lot of the concepts described by thermodynamics seem like common sense but there is a layer of math beneath the intuitive level that makes them very powerful at describing systems and making predictions. we won't get into the math but we should be able to describe these laws conceptually.

the first law described in the most basic way highlights conservation of energy energy is not created or destroyed it only changes forms, from potential energy to kinetic energy to heat energy, etc. while we have found this to be untrue on the quantum level, for chemists it does just fine. however there seems to be a preferred direction in which energy flows from one form to another.

in order to understand why we look at the 2nd law. the 2nd law introduces a new concept: entropy. entropy is quite difficult to understand but we can most easily describe entropy as disorder, and the 2nd law states that the sum of the entropies of a system and its surroundings must always increase.

in other words the entropy or the disorder of the universe is always increasing within a system there is also a tendency to go towards higher entropy. the classic analogy is that your bedroom will over time become messy but it won't suddenly become neat. another way to look at this is to say that entropy is a measure of how dispersed the energy of the system is amongst the ways that system can contain energy.

yet another way is to analogize entropic states to computer code. let's take for example an ionic solid compared to the same substance as a liquid. clearly the solid state is more ordered and the liquid state is more disordered, or higher in entropy.

to describe the solid state using computer code you would need to include terms that describe the geometry of the lattice, the intermolecular distances, the precise configuration of every molecule and many other things. but to describe the liquid state you would need to simply describe the volume of liquid and the shape of the vessel because the motion and configuration of the molecules are random. that's far less information that needs encoding which is a way of rationalizing why increasing the entropy of a system is thermodynamically favorable.

we can look at all kinds of processes to highlight entropic influence. heat will flow from a hot coffee cup into the table or your hand because the heat energy will be more disordered if more dispersed. this is why heat spontaneously flows from hot to cold and not the other way around.

entropy. the third law states that a perfectly crystalline solid at absolute zero has an entropy of zero as this is the most ordered state the substance can be in. entropy is measured in joules per kelvin.

note that entropy is not a measure of energy itself but of how energy is distributed within a system. it is enthalpy, the thermodynamic quantity we learned about before that is more accurately describing the energy of a system. as we will see enthalpy and entropy intricately relate to tell us something about the Gibbs free energy of a system.

G, or Gibbs free energy tells us whether a process will be spontaneous or not meaning if it will simply happen on its own change in Gibbs free energy is given by this equation which includes change in enthalpy, change in entropy and temperature. if delta G is negative the process is spontaneous, if positive it is nonspontaneous. so we can use this equation to see how a spontaneous process can be either enthalpically or entropically favorable or both but not neither.

for example if delta H is negative which means exothermic and energetically favorable, and delta S is positive which means an increase in entropy which is also favorable, a negative minus a positive will always be negative or spontaneous. if the opposite is true and both are unfavorable we have a positive minus a negative which will always be positive or nonspontaneous. if only one of the two is favorable we have to do some math.

if delta H is positive or endothermic, that energetic unfavorability could be outweighed by the other term if the process is entropically favorable, and since T is here this factor will increase with a larger T so entropically favorable processes are more likely to be spontaneous at higher temperatures. conversely if it is energetically favorable but entropically unfavorable the entropic unfavorability will be minimized at lower temperatures. this is a very important equation to understand because it describes all of the spontaneous processes in the universe there are those who incorrectly use entropy and the second law of thermodynamics to imply that order can't happen spontaneously, but we just showed that entropically unfavorable processes can be spontaneous at lower temperatures if they are energetically favorable.

an example of this is soap. you need soap to wash nonpolar dirt and grime off your hands because they are immiscible with polar water molecules, but soap molecules have polar heads and long nonpolar tails which allows them to spontaneously form structures called micelles. these are spheres where the soap molecules orient themselves with the polar heads facing out in order to maximize ion-dipole interactions with water molecules that bring the system to a lower energy and the nonpolar tails will all face in trapping the dirt by making a network of van der Waals interactions.

the dirt trapped in the micelles washes away because the micelle as a whole is water-soluble, due to the polar heads facing out. that's how soap works and that's also how highly ordered structures can form spontaneously if by enthalpically favorable or energy storing processes. in this way systems can defy entropy on the small scale but the 2nd law does hold true in that the entropy of the universe is always increasing.