Question

For the process to occur under adiabatic conditions (1) \(\Delta T=0\) (2) \(\delta q=0\) (3) \(\Delta P=0\) (4) \(\delta w=0\)

Short answer

The correct condition for an adiabatic process is \( \delta q=0 \)).

Step-by-step solution

Understand adiabatic conditions

In an adiabatic process, there is no heat exchange between the system and its surroundings. This implies that the heat transfer \( \delta q=0 \)).

Analyze given options

Consider each given option to identify which one correctly describes an adiabatic process: (1) \( \Delta T=0 \)), (2) \( \delta q=0 \)), (3) \( \Delta P=0 \)), (4) \( \delta w=0 \)).

Determine correct condition

\( \Delta T=0 \)) implies that temperature remains constant, which is not necessarily true for an adiabatic process. \( \Delta P=0 \)) suggests constant pressure, which also doesn't generally apply to adiabatic processes. \( \delta w=0 \)) would indicate no work done, which is not a distinctive feature of adiabatic processes. The true defining feature is that \( \delta q=0 \)), meaning no heat transfer.

Key concepts

thermodynamics

Thermodynamics is the study of energy, heat, and work, and how they interact and transform within systems. This field explores the fundamental principles governing physical and chemical processes.
Understanding thermodynamics requires knowing a few key concepts:

• System: The part of the universe we are focusing on.
• Surroundings: Everything outside the system.
• State Functions: Properties that depend only on the state of the system, such as pressure (P), volume (V), and temperature (T).
• Process: The path taken from one state to another.

The first law of thermodynamics, also known as the law of energy conservation, states that energy cannot be created or destroyed, only transformed. It can be mathematically expressed as:
\[ \text{dU} = \text{dq} - \text{dw} \] Here, \( \text{dU} \) represents the change in internal energy, \( \text{dq} \) is the heat added to the system, and \( \text{dw} \) is the work done by the system. This principle forms the foundation for understanding various thermodynamic processes, including adiabatic processes.

heat transfer

Heat transfer is the movement of thermal energy from one object or substance to another due to a temperature difference. It's essential to understand how heat interacts with matter in thermodynamic processes. Heat can be transferred in three ways:

• Conduction: Direct transfer through a substance due to temperature gradients. Imagine touching a hot pan handle.
• Convection: Transfer via fluid motion, such as boiling water where warm water rises and cooler water sinks.
• Radiation: Transfer through electromagnetic waves, like the heat from the sun.

With these methods, systems can exchange heat with their surroundings. However, in an adiabatic process, no heat transfer occurs. This means \( \text{dq} = 0 \), a defining characteristic of adiabatic conditions. Consequently, any change in the system's energy must come solely from work done on or by the system, not from heat exchange.

adiabatic conditions

Adiabatic conditions refer to processes where there is no heat exchange between the system and its environment. In other words, \( \text{dq} = 0 \). This concept is crucial in thermodynamics for understanding certain types of processes.
Adiabatic processes can be either reversible or irreversible:

• Reversible Adiabatic Process (Isentropic Process): Occurs without entropy change. It represents an ideal scenario where the process is both adiabatic and completely reversible.
• Irreversible Adiabatic Process: Involves changes in entropy and usually happens quickly and spontaneously.

Key characteristics of adiabatic processes include:

• When a gas expands adiabatically, it cools down because no heat is added, and it does work on its surroundings.
• When compressed adiabatically, it heats up since work is done on the gas, and no heat is lost to surroundings.

A practical example is the rapid compression or expansion in a piston-cylinder mechanism. Considering adiabatic conditions helps simplify complex thermodynamic analyses.