Thank you for your careful consideration; thank you also for your thoughtful responses. And thank you for directing me towards the forum rules. I will carefully consider them.You would do well to review the forum rules on personal speculation. Your rigid adherence to false personal positions in the face of careful correction is not appreciated.
The situation when releasing compressed air through a nozzle complicated. See this link for some of the complications. There is a difference between a reversible expansion and a free expansion and between a real gas and an ideal gas.
However, the conclusion in this specific case is correct. The can gets cold because the gas remaining in the can has done work, pushing exhausted gas toward the nozzle opening. The expansion of the portion of the gas that remains in the can counts as "reversible".
I don’t believe I’m being rigid. I suppose no pigheaded person does. I once argued with my high school Physics teacher about why I couldn’t make a bicycle generator that would push the bicycle until he explained the problem in a way I could understand. I appreciated my teachers patience with me, just as I appreciate you and the others now.
But I don’t see how my original idea has been addressed in a way that I can understand. If you have nine cats in a box and you decrease the size of the box you still have nine cats in that box. If you want to argue that decreasing the size of the box will require adding more cats, I will concede that. You could even argue that the reduction of the box is exactly proportional to the amount of cats being added. My point is that changing the size of the box has increased the gradient of the original amount of cats with respect to those outside the box. Again, irrespective of the cats that were added to reduce the size of the box.
I always try to be patient with people who are not as smart as me. Believe it or not there really are people not as smart as me.