Main Question or Discussion Point
Assuming that the gas in these processes is an ideal one, is the change in internal energy in an isochoric process (volume remaining constant) the same as the change in internal energy of isobaric process (pressure remaining constant)? Mathematically I can derive that they're equivalent, but what's the physical reason behind that? Does it have something to do with the temperature of the gas? My reasoning is this: if you start from the a point on a PV diagram (I'll call it A) and move up in an isochoric process to a point B, and then starting from A if you move right to a point C in an isobaric process, you end up at an isotherm that both A and C lie on if you add equal amounts of heat Q in both AC and AB, and that's why their changes in internal energy are the same. Is my reasoning correct?