A mole of an ideal gas undergoes a reversible isothermal...

A mole of an ideal gas undergoes a reversible isothermal expansion from volume $V_1$ to $2 V_1$. (a) What is the change in entropy of the gas? (b) What is the change in entropy of the universe? Suppose the same expansion takes place as a free expansion: (a) What is the change in entropy of the gas? (b) What is the change in the entropy of the universe?

A mole of an ideal gas undergoes a reversible isothermal expansion from volume $V_1$ to $2 V_1$.
(a) What is the change in entropy of the gas?
(b) What is the change in entropy of the universe?

Suppose the same expansion takes place as a free expansion:
(a) What is the change in entropy of the gas?
(b) What is the change in the entropy of the universe?

Key Concepts

Isothermal Process

An isothermal process is one that occurs at a constant temperature, meaning that the internal energy of an ideal gas remains constant. In such processes, any work done by the gas is exactly compensated by heat transfer, maintaining temperature equilibrium throughout the process.

Reversible Process

A reversible process is an idealized thermodynamic transformation that happens infinitely slowly, ensuring that the system is always in equilibrium with its surroundings. In reversible processes, every intermediate state of the system is a state of thermodynamic equilibrium, and the total entropy change of the combined system plus environment is zero.

Irreversible Process

An irreversible process is one that deviates from equilibrium and cannot be reversed without leaving a net change in the system or surroundings. A free expansion, where a gas expands into a vacuum without doing work or exchanging heat, is a common example of an irreversible process; despite no heat transfer, the entropy of the system increases due to the production of entropy during the expansion.

Entropy Change

Entropy change is a measure of the dispersion of energy and the increase in the number of accessible microstates as a system undergoes a process. For an ideal gas undergoing expansion, entropy change can be calculated using the natural logarithm of the ratio of the final to initial volumes when temperature remains constant, reflecting the increased disorder of the system.

Entropy of the Universe

The entropy of the universe includes the entropy changes of both the system and its surroundings. In any reversible process, the entropy change of the universe is zero, as the increase in the system's entropy is balanced by a corresponding decrease in the surroundings' entropy. In contrast, irreversible processes generate extra entropy due to internal production, leading to a net increase in the total entropy of the universe.

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