In an adiabatic process, heat transfer doesn't occur and hence $\Delta U=-W$ (an increase in internal energy due to work done on the system or a decrease in internal energy due to work done on the surrounding).
My textbook then says (for monatomic gas) adiabatic process takes the form: $PV^{5/3} =$ constant
What does this equation means? From my understanding, "$PV^{5/3} =$ constant" pinpoints to a specific Pressure and Volume of the system and implies a specific Temperature of the system. This is pretty much equivalent to $PV=nRT$ where a specific Pressure and Volume implies a specific Temperature of the system.
But in an Adiabatic process the Temperature, Pressure and Volume can change (otherwise if nothing changes, what's the point of there being a process? and from $\Delta U=-W$ there should be something going on, the temperature should change which will cause a change in the volume of the system [but not a change in pressure since we're assuming the process is quasi-static and thus pressure is constant]) and thus what is the meaning of the equation? Why is this equation specific to adiabatic process?
Best Answer
The equation for adiabtic process you wrote does not fix both volume and pressure...you can pick any pressure and then and only then, the volume is fixed, and it is calculated via formula you wrote. I can give you this example: lets say that we observe isotermic process, that is, with constant temperature, and we know that for this process there is a formula PV=const. That does not mean that both P and V are fixed. Lets say, PV=2. Then, we can write: P=2/V. So, if V=8, for example, P= 2/8=0.25. Same thing for adiabtic process with the difference that the dependence goes with -5/3 and not -1 like here.