Question

A gaseous system changes from state \(\mathrm{A}\left(P_{1}, V_{1}, T_{1}\right)\) to \(\mathrm{B}\left(P_{2}, V_{2}, T_{2}\right)\) to \(\mathrm{C}\left(P_{3}, V_{3}, T_{3}\right)\) and finally from C to \(\mathrm{A}\). The whole process may be called (1) Reversible process (2) Cyclic process (3) Isobaric process (4) Spontancous process

Short answer

Cyclic process

Step-by-step solution

Understanding the problem

The problem describes a gaseous system that undergoes a series of state changes: from state A \((P_1, V_1, T_1)\) to state B \((P_2, V_2, T_2)\), to state C \((P_3, V_3, T_3)\) and then back to state A. We are to determine the nature of this entire process. Given the options, we need to identify whether the process is reversible, cyclic, isobaric, or spontaneous.

Considering the definition of a cyclic process

A cyclic process is one in which a system returns to its initial state after undergoing a series of changes. Here, the system returns to state A after passing through states B and C. Since state A is the starting and ending point of the process, this implies the process is cyclic.

Evaluating other processes

It's important to consider other types of processes to be thorough. A reversible process is one that can be reversed by infinitesimal changes in conditions. An isobaric process is one where pressure remains constant. A spontaneous process occurs naturally without needing to be driven by external forces. None of these definitions adequately describe the given process based on the system returning to its initial state.

Confirming the correct answer

By the process of elimination and understanding of definitions, the whole process described fits the definition of a cyclic process. Therefore, the correct option is (2).

Key concepts

state changes

In thermodynamics, a state change occurs when a system transitions between different sets of properties. For a gas, these properties often include pressure (P), volume (V), and temperature (T). In the given problem, the gaseous system changes from state A (P_1, V_1, T_1) to state B (P_2, V_2, T_2), then to state C (P_3, V_3, T_3), and finally returns to state A. This means that the process involves specific changes in the system's pressure, volume, and temperature at each state.

• Pressure (P): Force exerted by the gas per unit area.
• Volume (V): Space occupied by the gas.
• Temperature (T): Measure of the thermal energy within the system.

Understanding state changes is crucial because each state is defined by specific values of these properties. When the system returns to its original state, as in the given problem, it completes a cycle of changes, indicating a cyclic process.

reversible process

A reversible process is an idealized concept where a system's changes can be reversed by infinitesimal modifications in conditions. In reality, true reversible processes do not exist because all real processes involve some form of irreversibility due to factors such as friction, unrestrained expansion, and heat loss.
In a reversible process:

• Every stage remains in thermodynamic equilibrium.
• The transformations occur infinitely slowly so the system can adjust and maintain equilibrium.
• No net change occurs in the external environment if the process is reversed.

In the given exercise, the series of state changes from A to B to C and back to A is not explicitly stated to be slow or reversible, indicating the process described is more likely a cyclic process rather than a reversible one.

isobaric process

An isobaric process is characterized by a constant pressure throughout the entire transition. For instance, when a gas is heated or cooled in a container that can expand or contract (like a piston), and the pressure inside the container remains the same, this is an isobaric process.
Key features of an isobaric process:

• Pressure (P) remains constant.
• The volume (V) of the gas changes to accommodate the energy transfer involved with temperature changes.
• Can be represented on a Pressure-Volume (P-V) diagram as a horizontal line.

In the problem, the presence of distinct states A, B, and C with different pressures and temperatures implies that the process is not isobaric since the pressure does not stay constant between these states.

spontaneous process

A spontaneous process occurs naturally without external intervention. These processes are driven by factors such as entropy increase and energy minimization, making them naturally favorable.
Characteristics of spontaneous processes:

• They proceed without any external influence once started.
• They often involve a release of energy (e.g., heat, light).
• They usually lead to an increase in disorder or entropy in the system.

The process described in the problem involves a series of state changes where the system cyclically returns to its original state. This description does not suggest that the process occurs spontaneously. Instead, it is more accurately classified as a cyclic process, deliberately orchestrated to return to the initial state A.