Hi there, after years of blissful unawareness, I suddenly managed to find a simple yet, annoyingly perplexing question regarding our old friend, the adiabatic process. Let's look at the facts. Any textbook will tell us that in an adiabatic process no heat is exchanged between the system and its surroundings (1). Any textbook will also tell us that the equation that governs such a process is PV^gamma = constant (2). Finally, that textbook will also tell us that the internal energy of a gas is dependent on its temperature ONLY (3). We have all the actors on stage, now let's hear their story. 2 tells us that, as volume expands, pressure will drop. A quick calculation involving PV=NRT will show that temperature follows suit. This is the most classic textbook case of basic thermodynamics, an expanding gas cools down. Now, 3 will tell us that, since temperature drops, surely, the internal energy drops as well. So, since energy cannot be destroyed, it must have gone somewhere right? But 1, says that in the adiabatic process, no heat is exchanged between the system and its surroundings. Now, the first law leaves a loophole for energy to leave in the form of work. But an expanding gas does not always do work. Imagine the case of a volume of gas freely expanding in vacuum for example, no work done yet temperature drops. Why? As far as I can see, it seems that PV^gamma=constant seems to be in direct contradiction with the first law since it implies a drop in internal energy of an expanding gas with no visible route for this energy to leave the gas. This is silly but try as I might, I cannot see where the flaw in my logic is. If any of you guys can point out the obvious to me I 'll be very grateful.