Counterdiabatic formalism of shortcuts to adiabaticity

When an ideal gas is compressed adiabatically, that is, without adding heat, work is done on it, and its temperature increases. In an adiabatic expansion, the gas does work, and its temperature drops. Adiabatic compressions actually occur in the cylinders of a car, where the compressions of the gas-air mixture take place so quickly that there is no time for the mixture to exchange heat with its environment. Nevertheless, because work is done on the mixture during the compression, its...

Free expansion of a gas is an adiabatic process. However, there are few differences between free expansion and adiabatic expansion. During free expansion, no work is done, and there is no change in internal energy. But, for an adiabatic expansion, work is done, and there is a change in internal energy. During an adiabatic process, the relation between the pressure and volume is obtained from the condition for the adiabatic process, that is, 

Consider the adiabatic compression of an ideal gas in the cylinder of an automobile diesel engine. The gasoline vapor is injected into the cylinder of an automobile engine when the piston is in its expanded position. The temperature, pressure, and volume of the resulting gas-air mixture are 20 °C, 1.00 x 105 N/m2, and 240 cm3 , respectively. The mixture is then compressed adiabatically to a volume of 40 cm3. Note that, in the actual operation of an automobile engine, the compression is not...

The hypothetical Carnot cycle consists of an ideal gas subjected to two isothermal and two adiabatic processes. Since the internal energy of an ideal gas depends only on its temperature, which is the same before and after the completion of the Carnot cycle, there is no change in its internal energy. Hence, using the first law of thermodynamics, the total heat exchanged by the ideal gas equals the total work done. Thus, we can quantify the efficiency of the Carnot cycle via the heat exchanged...

Converting work to heat is an irreversible process, and the purpose of a heat engine is to reverse the effect partially. Heat engines aim to increase the efficiency of the reversal, that is, maximize the work retrieved from heat. If the efficiency of a heat engine were 100%, it would imply reversing the process completely without introducing any other effect. Thus, it would violate the second law of thermodynamics.
What could be the theoretical limit to the efficiency of a heat engine? The...

The Diels–Alder reaction is thermally reversible, meaning that the reaction reverts to the starting diene and dienophile under suitable temperatures. The forward reaction gives a cyclohexene derivative and is favored at low to medium temperatures. The reverse process, also called retro-Diels–Alder reaction, is a ring-opening process favored at high temperatures.