Problem 8 - Advanced Problems in Physical Chemistry for Competitive Examinations

Question

If a closed system has adiabatic boundaries, then at least one boundary must be (a) permeable (b) imaginary (c) movable (d) fixed

Step-by-Step Solution

Answer

The correct answer is (c) movable since a closed adiabatic system can perform work without heat transfer, often requiring a movable boundary.

Step 1 - Understanding the Adiabatic Process

In thermodynamics, an adiabatic process is one that occurs without transfer of heat or mass between a system and its surroundings. Since the system is closed, there is no mass transfer. The adiabatic process requires boundaries that prevent heat transfer.

Step 2 - Analyzing the Options

Option (a) refers to a boundary that allows matter to pass through, which is unrelated to adiabatic conditions. Option (b) implies that the boundary isn't tangible and can't impact physical processes. Option (d) suggests a boundary that neither moves nor allows energy or matter transfer; this is possible in an adiabatic system but doesn't encompass the necessary condition for adiabatic processes. Option (c) 'movable' is significant because, in adiabatic processes, work can be done by or on the system, which would often require a movable boundary, such as a piston in a cylinder, to allow for volume change without heat exchange.

Step 3 - Choosing the Correct Option

Considering the nature of an adiabatic process and the characteristics of the options provided, the boundary of a closed adiabatic system can be fixed; however, having a movable boundary allows the system to do work or have work done on it in the absence of heat transfer, which is characteristic of adiabatic processes. Therefore, the correct choice is (c) movable.

Key Concepts

Thermodynamics

Thermodynamics is a branch of physics that deals with the relationships between heat and other forms of energy. In essence, it involves the study of energy, entropy, and the laws that govern the transfer of energy within and between systems. This area of study is fundamental to understanding how systems respond to changes in temperature, pressure, and volume.

At the heart of thermodynamics lie four main laws which outline how energy moves and converts from one form to another. The zeroth law establishes thermal equilibrium and the concept of temperature. The first law, also known as the law of energy conservation, states that energy cannot be created or destroyed, only transformed. In the example of an adiabatic process, this law is crucial as it points to the work done by or on the system in the absence of heat transfer.

Heat Transfer

Heat transfer is a discipline of thermal engineering that concerns the movement of heat between physical systems. Heat can be transferred via three main mechanisms: conduction, convection, and radiation. During conduction, heat transfer occurs through a material or from one material to another when they are in direct contact. Convection describes the transfer of heat through a fluid (such as air or liquid) caused by molecular motion. Radiation is the transfer of energy through electromagnetic waves.

In the context of adiabatic processes, the term 'adiabatic' literally means 'no heat transfer'. This signifies that all energy changes in the system are attributed to work rather than heat exchange with the surroundings. This is a key concept in the study of thermodynamics and often involves idealized scenarios that, while rare in everyday situations, provide crucial insights into the theoretical limits of energy conservation and conversion.

Closed System

A closed system in the realm of thermodynamics is a physical system that does not allow matter to enter or leave, but may permit energy to be transferred in the form of heat or work. In other words, it can exchange energy but not mass with its surroundings. The Earth's atmosphere can be considered a closed system because it allows sunlight (energy) to enter but retains its gases (mass) due to gravitational forces.

The concept of a closed system is particularly pertinent when discussing adiabatic processes since a truly adiabatic system must be closed in order to ensure no heat is transferred. As noted in the textbook exercise, the adiabatic process within a closed system typically requires a movable boundary to facilitate work without heat transfer. This aligns with the broader definition of a closed system, as it focuses on transformations and exchanges of energy while preserving the system's mass.