Enthalpy, Entropy and Free Energy

Once you know how to calculate various Thermodynamic quantities involved in a reaction, the next thing you need to determine is whether the reaction is feasible or not. Will it occur as you imagine it or will nothing happen. How to determine it is what we will be covering in this post.

The basics that you need to know are :

1. Knowledge of First Law of Thermodynamics 
2. How to calculate ΔQ, ΔW and ΔU for various processes.
3. Concept of C_p and C_v

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Enthalpy is quite abstract, so I won't bother copy pasting its physical significance. For now, just remember that Enthalphy is similar to Q ( The heat supplied to a system ).
Mathematically : H = U+PV
So this would give me that ΔH=ΔU+PΔV+VΔP

Points to Note :

1. ΔQ=ΔU+PΔV  ( There is no vΔP term which is present in Enthalpy ).
2.  If ΔP=0 then ΔH=ΔQ. So in an Isobaric Process they are the same thing.
3. Heat Capacity=ΔQ/ΔT. At Constant pressure Heat Capacity= ΔH/ΔT= C _p
4. ΔH < 0 for an exothermic reaction and is positive for an endothermic reaction.
5. Change in Enthalpy can be considered a representation of the total Energy Change taking place in a reaction.
6. You may be given the ΔH values of different reactions and asked to find the ΔH value of some other reaction.

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Second Law of Thermodynamics : "For a heat engine to produce continuous mechanical work it must exchange heat with two bodies at different temperatures, by absorbing heat from the hot body and discarding it into the cold body."
That is the complicated form of the second law!
What that implies is that it is impossible for a heat engine ( i.e. a thermodynamic system ) to have 100% efficiency. If you look at this from an entropy point of view, the statement would be, " In any Spontaneous process, Entropy of the universe cannot decrease. "
Mathematically : ΔS >= 0.

Entropy is a measure of the randomness of a system. The more the Entropy, the more randomness there is in the system and the more " Useless Energy " is present in a system. And entropy never decreases. If  there's a reaction in a test tube that has a negative  ΔS_system then the corresponding ΔS_surroundings due to that reaction will be such that ΔS_system+ΔS_surroundings >=0. The Second Law will always hold.
Entropy and Enthalpy are both Extensive properties.

Important points related to entropy :

1. Mathematically ΔS=Q_rev  /T. Here Q_rev is the heat supplied reversibly to the system.
2. Suppose a system is going from a state A to a state B. There can be numerous ways of achieving this transition.
3. To calculate ΔS Suppose the gas goes from ( P₁, V₁, T₁ ) to ( P₂, V₂, T₂ ).
4. dQ = dU + dW = nC_v .dT  + P.dV = nC_v dT + (nRT.dV)/V
5. dS = dQ_rev /T = (nC_v. dT) /T + (nR.dV)/V
6. On Integrating you will obtain ΔS= nC_v Ln(T₂ / T₁ ) + nR.Ln (V₂ / V₁ )

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So now we know how to calculate ΔS and ΔH for a given reaction. The thing that we would now like to know is whether a reaction is spontaneous or not. This is what scientists too must have been trying to figure out.

To make sure that a process is spontaneous we to confirm whether ΔS_total is positive or not. We can easily calculate ΔS_system but unfortunately ΔS_surroundings is not that easy to determine.

If we make simplifications, we can consider the change in temperature of the surroundings due to our reaction to be zero. And if heat Q is supplied to the system, heat -Q is supplied to the surroundings, therefore ΔS_surroundings = -Q/T_surroundings . However our assumption that temperature of surroundings does not change, is not strictly valid.

Therefore to determine whether a reaction is spontaneous or not, we measure the change in Gibb's Free energy. The main formula used is :
ΔG = ΔH - TΔS
Here ΔG is the change in Free Energy. A reaction is spontaneous if ΔG < 0. This condition is necessary and sufficient for determining spontaneity of a reaction. There is a derivation for this formula but it isn't really required. Just remember the formula.

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So now that you've read this post can you explain how the picture at the beginning of the post is related to the the topic?
Also, If the Free Energy of the Universe is constantly decreasing, what will happen when there's no Free Energy left in the World?

(P.S. Memorize Everything that's in blue )

Note: You need to read a book too. This post is only meant to give you a better understanding of the topic. You still need to at least go through the headings in a book. Thermodynamics is my weak area so I cannot guarantee that I've covered everything.