Consider a process in which an ideal gas changes from state 1 to state 2 in such a way that its temperature changes from 300 K to 200 K. (a) Does the temperature change depend on whether the process is reversible or irreversible? (b) Is this process isothermal? (c) Does the change in the internal energy, \(\Delta E,\) depend on the particular pathway taken to carry out this change of state?

A reversible process is a process that can be reversed by an infinitesimal change in the external conditions without any dissipation of energy or change in the surroundings. An irreversible process, on the other hand, is any process that, after the process has occurred, it is impossible to return both the system and its surroundings to their original states. The question asks if the temperature change, from 300 K to 200 K, depends on whether the process is reversible or irreversible. For an ideal gas, the temperature change depends only on the initial and final states and not on the pathway taken (reversible or irreversible). Therefore, the temperature change does not depend on whether the process is reversible or irreversible.

An isothermal process is a process in which the temperature of the system remains constant throughout the process. Since the temperature changes from 300 K to 200 K, this process is not isothermal because there is a change in temperature.

The change in internal energy \((\Delta E)\) for an ideal gas depends only on the initial state and the final state and not on the particular pathway taken to carry out this change of state. This means that the internal energy change is a state function and path-independent. Regardless of whether the process is reversible, irreversible, or happens through a combination of various processes, the \(\Delta E\) will remain the same as long as the initial and final states are the same.