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Relative Pressure and Relative Specific Volume

One issue we run into with the isentropic case for variable specific heats is that we don't immediately get a nice relationship between pressure and temperature. The integral still remains afterwards. We still have that absolute entropy term to deal with. Relative pressure is a way of getting rid of that. It allows us to connect the state before and after an isentropic process by creating a new value called either Relative Pressure or Relative Specific Volume. You can look up your relative pressure before the process, then you will discover that relative pressure changes by the same ratio as regular pressure. This gives you the relative pressure after the process. From that you can get your temperature, internal energy, etc.