91Ó°ÊÓ

Entropy is a fundamental concept in thermodynamics that quantifies the degree of disorder or randomness in a system.
In more straightforward terms, it measures how spread out or chaotic energy is in a system.
When an ideal gas expands isothermally (at constant temperature), its entropy increases because the gas molecules have more space to occupy and hence can be arranged in more ways.
This is because:

• The number of microstates, or possible configurations, accessible to the gas increases.
• More energy paths lead to greater disorder.

Consequently, in an isothermal process, where temperature remains constant but volume increases, the system absorbs heat, causing an increase in entropy.
For example, if an ideal gas does work on its surroundings by expanding isothermally, as in the original exercise, it indicates that heat flows into the system, further increasing entropy.

An isothermal process is a type of thermodynamic process where the temperature remains constant.
This means any heat added to the system is used to do work, without altering the internal energy.
Here’s why isothermal processes are significant:

• They often occur in slow processes where thermal equilibrium is maintained.
• Since temperature is constant, the internal energy of an ideal gas remains unchanged.

In isothermal expansion, like in the given exercise:

• The gas expands, doing work on the surroundings.
• Heat is added to the gas to keep the temperature constant.
• The entire heat energy is transferred to the work done, typically measured by the equation \( Q = W \).

Understanding this concept can explain why the given expansion does not change internal energy and why the heat supplied results directly in the work done, leading to an increase in entropy due to energy redistribution.

The Ideal Gas Law is a cornerstone in understanding how gases behave under various conditions.
Its formula is expressed as:

• \( PV = nRT \)
• Where \( P \) is pressure, \( V \) is volume, \( n \) is the number of moles, \( R \) is the gas constant, and \( T \) is temperature in Kelvin.

In the context of the problem, this law helps explain how, despite temperature being constant during an isothermal expansion, volume changes interact with pressure changes:

• As the gas expands, volume \( V \) increases.
• To maintain the product \( PV \) at constant \( nRT \), pressure \( P \) must decrease.
• In essence, while one property increases, another must decrease to keep the equation balanced.

This principle is vital for solving many thermodynamic problems, as it provides a clear relationship between different properties of the gas, such as in our original exercise with isothermal processes, ensuring that even as volume changes, the other variables adjust appropriately to maintain equilibrium.