Question

Indicate which of the following processes are reversible. (a) Nitrogen and oxygen gases diffuse to give a homogeneous mixture. (b) Ice sublimes at \(-5^{\circ} \mathrm{C}\) and 1.0 atm. (c) Energy as heat is transferred to the surroundings from a mixture of ice and water at \(0^{\circ} \mathrm{C}\) causing more ice to form. (d) Bromine evaporates and the gaseous molecules diffuse into the atmosphere.

Short answer

Only process (c) is reversible.

Step-by-step solution

Understanding Reversible Processes

A reversible process is one that can be reversed by an infinitesimally small change in a variable without any loss in energy or increase in entropy. In a reversible process, the system and surroundings are always in thermodynamic equilibrium.

Analyze Process (a)

In process (a), nitrogen and oxygen gases diffuse to form a homogeneous mixture. Diffusion is a spontaneous process that increases entropy and is irreversible because returning to the original state (with gases initially separated) would require an external intervention.

Analyze Process (b)

In process (b), ice sublimes at \(-5^{\circ} \mathrm{C}\) and 1.0 atm. Sublimation is the transition from solid to gas and occurs spontaneously with an increase in entropy, making this an irreversible process in this context due to the spontaneous nature and lack of equilibrium conditions.

Analyze Process (c)

In process (c), heat is transferred to excess ice in the ice-water mixture, causing more ice to form at \(0^{\circ} \mathrm{C}\). This process occurs under equilibrium conditions at the melting/freezing point and can be reversed by an infinitesimal change in temperature, making it a reversible process.

Analyze Process (d)

In process (d), bromine evaporates and the gases diffuse into the atmosphere. This diffusion is a spontaneous process leading to an increase in entropy, which is typically irreversible, as reversing it (condensing bromine back and re-separating it from the atmosphere) would require significant intervention.

Key concepts

Entropy

Entropy is a fundamental concept in thermodynamics, representing the degree of disorder within a system. When molecules spread out or mix, such as nitrogen and oxygen forming a homogeneous mixture, the system becomes more disordered, or chaotic, leading to an increase in entropy.

Entropy is linked to the second law of thermodynamics, which states that the total entropy of an isolated system always increases in a spontaneous process. This increase is why processes like diffusion or sublimation, where molecules move from a state of order to disorder, are characterized as irreversible.

Entropy can appear complex, but at its core, it marks the direction in which natural processes occur: from order to disorder, unless external work is done to reverse this tendency. In practice, understanding how entropy increases helps in predicting the direction and spontaneity of processes.

Thermodynamic Equilibrium

Thermodynamic equilibrium occurs when a system's properties remain constant over time unless disrupted by an external influence. In equilibrium, the system and its surroundings are in perfect balance. Changes can occur, but only with infinitesimally small shifts that don't alter the overall balance.

Consider ice melting at its freezing point of 0°C. When ice and water coexist at this point, they are in equilibrium. The conversion between ice and liquid water can be reversed with minute changes in temperature, qualifying this process as reversible. The highly controlled conditions ensure no net change in entropy, distinguishing reversible processes from those that involve larger, spontaneous changes.

For reversible processes, thermodynamic equilibrium ensures that both the system and its environment remain unchanged if the process were reversed, making them an idealized but essential concept in thermodynamics.

Spontaneous Processes

Spontaneous processes are natural occurrences that proceed without external interventions. A key aspect of these processes is the association with an increase in entropy.

Take the example of bromine evaporation and its diffusion into the atmosphere. This is a spontaneous process, as the bromine molecules naturally spread out into the available space, enhancing randomness and increasing the system's entropy. Similarly, the diffusion of gases like nitrogen and oxygen to form a mixture occurs spontaneously, driving the system toward equilibrium.

Such processes often involve irreversibility in natural conditions since returning to the previous, more ordered state would require external energy. Understanding spontaneous processes is crucial in thermodynamics, as it underscores the natural tendency towards disorder and the prerequisites for maintaining order or reversing these processes.