To calculate the work done by an adiabatic process, we were given this calculation method:
I don't understand where the quotient of the volumes with the adiabatic coefficient as an exponent in the integral comes from in the first line. The definition of work is actually just the integral -∫pdV
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The problem with a simple integral is that you are integrating over the volume, but you do not first know how the pressure depends on the volume. That’s why you use one of the adiabatic equations:
Your integral will be:
Therefore, you simply press your “current” p during integration over the “current” volume. Since you know the initial value of both volume and pressure (probably), this is not a problem.