The diagram shows three isotherms for an ideal gas, with T₃-T₂the same as T₂-T₁. It also shows five thermodynamic processes caried out on the gas. Rank the processes in order change in the internal energy of the gas, least to greatest.

Question

Quizplus · Accepted Answer

The internal energy is directly proportional to the temperature of the gas. As the isotherms are equally spaced, each representing a constant temperature, we can say that the internal energy of the gas is the same at all points on a given isotherm. Looking at the processes, we can see that Process V involves a horizontal movement along the highest isotherm. This means the temperature remains constant and so does the internal energy. Therefore, Process V has zero change in internal energy. Processes I, III, and IV all involve horizontal movements along the isotherm T₂. As this isotherm has a higher temperature than the others, these processes result in an increase in internal energy. However, we cannot distinguish between them in terms of the change in internal energy as they all follow the same path on the same isotherm. Finally, Process II involves going from the point U1 to U2 along the isotherm T₁. As this is a lower temperature than the previous isotherm, this process results in a decrease in internal energy. Therefore, the ranking of processes from least to greatest change in internal energy is: V (zero change), then I, III, and IV tied (same change), then II.

The Diagram Shows Three Isotherms for an Ideal Gas, with T3-T2

The Diagram Shows Three Isotherms for an Ideal Gas, with T₃-T₂