Process 1. The gas’s pressure is then reduced as its volume is increased in the process labeled 1, which is immediately above. The gauges
and piston position in Concept 2 show the state of the engine at the end of the process. The temperature does not change during this process.
During the first process, the amount of heat added to the engine equals the work done on the piston because the internal energy and
temperature of the gas do not change. The ideal gas law must be obeyed, so as the volume increases, the pressure decreases; their product
remains constant at each point along the path. Path 1 reflects one path by which the gas can change from its initial to its final state.
Process 2, step a. Now we show a different process by which the gas can be caused to move between the same two states. To make the
comparison clearer, we continue to show path 1 on the graph. The second process starts with the same pressure, volume and temperature as
before. This process has two distinct steps. In the first step, labeled 2a in the graph above, heat energy flows into the gas from the hot reservoir
as before. This increases the internal energy of the gas (as indicated by the increase in temperature). The graph is horizontal, indicating a
constant pressure. We could maintain the pressure by having the gas press against a constant weight.
Process 2, step b. Next, since we have the same volume that was reached by the path 1 process, we lock the piston into place, keeping the
volume constant. The pressure is too high, so we allow heat to flow out to the cold reservoir. This decreases the temperature of the gas, and at
this fixed volume, this means the pressure must decrease proportionally. You see this step labeled 2b in the graph above.
This two-step process arrives at the same final pressure-volume point as the first process, but in a different way. In the first, the gas’s
temperature remained constant while its pressure and volume constantly changed. In the second, first the volume was changed at constant
pressure, and then the pressure was changed at constant volume. The temperature changed during both of the steps of process 2.
The difference in the paths reflects an important point: Gases can change from one combination of pressure and volume to another by
experiencing different histories.
Both the processes sketched above obey the first law of thermodynamics and the ideal gas law. The first law is obeyed because there is the
samenet flow of heat into the engine in both cases. In process 1, all the heat is used for work, and the gas’s internal energy stays the same.
(To make the engine realistic, some heat should flow to the cold reservoir, since no engine is 100% efficient.) In process 2, more heat is added
during step 2a than in process 1, since in this step the gas does the same amount of work as in all of process 1 and its internal energy
increases. Heat flows out of the engine during step 2b, making the net heat into the engine the same for processes 1 and 2.
The ideal gas law is also obeyed. The product of the pressure and volume is always proportional to its temperature. For instance, on path 2b,
as the gas’s temperature decreases, its pressure decreases proportionally.
Process 1
Volume increases as pressure
decreases
Temperature does not changeProcess 2
a. Volume increases at constant
pressure; temperature increasesProcess 2
b. Pressure decreases at constant
volume; temperature returns to initial