Problem 72 - A Complete Resource Book in Chemistry for JEE Main

Question

Identify the state function among the following: (a) \(\mathrm{Q}\) (b) \(\mathrm{Q}-\mathrm{w}\) (c) \(\mathrm{Q} / \mathrm{w}\) (d) \(\mathrm{Q}+\mathrm{w}\)

Step-by-Step Solution

Answer

The state function is (b) Q-w.

Step 1: Understand the Concept of State Function

A state function is a property of a system that only depends on the current state of the system, not on the path taken to reach that state. Common state functions include internal energy (U), enthalpy (H), entropy (S), and free energy (G).

Step 2: Analyze Each Option

Let's examine each option to determine if it represents a state function: - (a) Q: Heat (Q) is typically a path function, meaning it depends on the specific process or path taken, not just the state. - (b) Q - w: This expression represents the change in internal energy. According to the first law of thermodynamics, it is defined as a state function. - (c) Q/w: This is a ratio of heat to work, which does not represent a state function as it depends on how the heat and work are applied. - (d) Q + w: Like Q, this combination is typically path-dependent.

Step 3: Select the State Function

Based on the analysis, \(\mathrm{Q} - \mathrm{w}\) is the only option that corresponds to a state function (change in internal energy). The others are path-dependent.

Key Concepts

Internal Energy

Internal energy is one of the fundamental concepts in thermodynamics. It represents the total energy contained within a system.
It is a type of state function. This means that its value is determined only by the state of the system, not the path taken to reach that state. Unlike path functions like heat or work that vary with the process, internal energy depends only on variables like temperature, pressure, and volume.

• Internal energy is commonly denoted as \( U \).
• It encompasses kinetic and potential energies at the molecular level.
• One important equation is \( \Delta U = Q - W \), describing how internal energy changes with heat (Q) added to the system and work (W) done by the system.

Understanding internal energy helps predict how systems react to changes, making it crucial for fields like chemistry and physics.

First Law of Thermodynamics

The First Law of Thermodynamics is a pivotal principle that lays the foundation for energy conservation.
It states that energy in an isolated system is constant; it can neither be created nor destroyed but only transferred or converted.

In mathematical terms, it is expressed as:

• \( \Delta U = Q - W \)

Here:- \( \Delta U \) is the change in internal energy,- \( Q \) is the heat added to the system, and- \( W \) is the work done by the system.
In essence, this law implies that when energy is applied as heat, part of it can do work while the rest changes the internal energy.
It emphasizes that total energy is constant and helps in understanding how energy transformations occur in both natural and engineered systems.

Path Function

Path functions are properties that depend on the specific processes used to change a system's state.
They contrast state functions, which rely only on the initial and final states of a system.

• Common path functions include heat (Q) and work (W).
• Unlike state functions, path functions can vary between different processes even if the initial and final states are the same.
• This dependency means there is no global property value, like a state function, for a path function.

Knowing whether a property is a path function helps determine how it will behave or be measured in different thermodynamic processes.
It allows scientists and engineers to carefully plan and predict the outcome of energy transfers.