Explained: Isentropic Relations 

In this video, we will go through the derivation of the isentropic relations. We will start with the combined 1st & 2nd law of thermodynamics (video [1] below for derivation of combined law). We will first assume a thermally perfect gas (video [2] below for explanation of e = e(T) and h = h(T)), and then later constrain the expression down for a calorically perfect gas (video [3] below for explanation about specific heats for TPG and CPG). To obtain the final isentropic relations, we will set the change in entropy equation equal to zero, and solve for the relationship between pressure, temperature, and density ratios between states 1 and 2.
===== RELEVANT VIDEOS =====
[1] : goo.gl/soiSr9
[2] : goo.gl/pdL6A8
[3] : goo.gl/hG2sJn
===== REFERENCES =====
► Notes by Matt MacLean
► Modern Compressible Flow, Anderson
► Elements of Gasdynamics, Liepmann and Roshko
► Gas Dynamics, Zucrow and Hoffman