Okay I think I get this but I just want to make sure: In a frictionless, fully insulated piston-cylinder arrangement, when an external force is applied to the piston and the gas inside the cylinder is compressed, the temperature of the gas remains constant, and none of the work done to the system (system being defined as the gas inside the cylinder) is converted to heat. Therefore the pressure of the gas can be calculated using the ideal gas law PV=nRT assuming T does not change, or by PV^k=constant for some k which is specific to the gas in the cylinder, (and is equal to the specific heat ratio cv/cp). The part about the temperature of the gas not changing had me hung up for a bit, because in the refrigeration cycle you can change the temperature of the refrigerant by altering the pressure. However, this is due entirely to the heat transfer with the surroundings: if the refrigerant is compressed in a cylinder, there are more molecular collisions with the cylinder walls, transferring heat out of the system, and lowering the temperature of the refrigerant. If the cylinder were completely insulated, heat transfer would not occur and the refrigerant would not change temperature. Right?