Question

Any series of operation so carried out that at the end, the system is back to its initial state is called (1) a cycle (2) an adiabatic process (3) a reversible process (4) A Boyle's cycle

Short answer

Option (1) - a cycle

Step-by-step solution

- Understanding the Question

The question is asking to identify a term that describes a series of operations that return a system to its initial state.

- Analyzing the Options

Option (1) - a cycle: A cycle refers to any series of operations after which a system returns to its initial state. This matches the description provided in the question.Option (2) - an adiabatic process: This process involves no heat transfer, but it does not necessarily mean the system returns to its initial state.Option (3) - a reversible process: This describes a process where the system can return to its initial state without any increase in entropy, but it is not a term that simply means returning to the initial state.Option (4) - A Boyle's cycle: This term refers to a specific type of process related to Boyle's Law, but it is not a general term for returning to the initial state.

- Selecting the Correct Answer

Based on the analysis, 'a cycle' best fits the description of a series of operations that return a system to its initial state. Thus, the correct answer is option (1).

Key concepts

Cycle

A cycle, in thermodynamics, refers to any sequence of processes that return a system to its initial state. This means that after completing a cycle, the system’s properties, such as temperature, pressure, and volume, are exactly the same as they were at the start.
One of the most familiar examples of a cycle is the Carnot cycle, where a system undergoes a series of expansions and compressions. The key point is that the system's final state is the same as its initial state, which can also be represented on a P-V (Pressure-Volume) diagram as a closed loop.
Important features of a cycle include:

• Returning to the initial state means no net change in the properties.
• The system can produce work (or require work) over the cycle.
• Different cycles have different efficiencies, based on how much work is produced per unit of heat energy absorbed.

Adiabatic Process

An adiabatic process is a thermodynamic process in which no heat is exchanged with the surroundings. This means that all the energy changes within the system are due to work done by or on the system, and not due to the transfer of heat.
A common example is the rapid compression or expansion of a gas, where there isn't enough time for heat to transfer. In mathematical terms, an adiabatic process can be described by the equation: \[ PV^\beta = \text{constant} \ \beta = \frac{C_p}{C_v} \]
Key features include:

• No heat exchange (Q = 0).
• Changes in internal energy are due only to work.
• Temperature can change even though no heat is added or removed.

Reversible Process

A reversible process is an ideal concept in thermodynamics where the process occurs infinitely slowly, allowing the system to remain in equilibrium at all stages. Because of this, the process can be reversed exactly, without leaving any change in either the system or the surroundings.
Reversible processes are important because they are the most efficient, meaning they can achieve the maximum possible work output. However, in real life, all processes are irreversible to some extent. Key points to understand include:

• Infinitely slow and no friction or dissipative forces.
• Restores both the system and surroundings to their original states without any net change.
• Used as a benchmark to compare real processes.

In mathematical terms, the change in entropy (\by the equation).\[ dS = \frac{dQ_{\text{rev}}}{T} \ \text{where } dQ_{\text{rev}}\text{ is the reversible heat transfer and } T \text{ is the absolute temperature.} \]

Boyle's Cycle

Boyle's Cycle refers to an idealized thermodynamic cycle that obeys Boyle's Law, where the product of the pressure and volume of a gas remains constant during a process (i.e., \( PV = \text{constant} \)).
This cycle forms the basis of many practical engines and refrigeration cycles. Boyle's Law is especially useful when dealing with processes where temperature is nearly constant (isothermal processes).
Characteristics include:

• It typically involves isothermal expansion or compression.
• The product of pressure and volume stays constant.
• While connected with Boyle's Law, it is not the same as simply returning a system to an initial state like a general thermodynamic cycle.

Knowing these underlying principles can help understand more complex thermodynamic cycles like the Carnot cycle or Otto cycle.