Problem 130 - Master Resource Book in JEE Main Physics

Question

Mark the correct options \(\quad\) [NCERT Exemplar) (a) A system \(X\) is in thermal equilibrium with \(Y\) but not with Z. System \(Y\) and \(Z\) may be in thermal equilibrium with each other. (b) A system \(X\) is in thermal equilibrium with \(Y\) but not with Z. System \(Y\) and \(Z\) are not in thermal equilibrium with each other. (c) A system \(X\) is neither in thermal equilibrium with \(Y\) nor with \(Z\). The systems \(Y\) and \(Z\) must be in thermal equilibrium with each other. (d) A system \(X\) is neither in thermal equilibrium with \(Y\) nor with \(Z\). The system \(Y\) and \(Z\) may be in thermal equilibrium with each other.

Step-by-Step Solution

Answer

Correct options: (b) and (d).

Step 1: Understanding Thermal Equilibrium

Thermal equilibrium occurs between systems if they are at the same temperature and no heat flows between them. According to the Zeroth Law of Thermodynamics, if system A is in thermal equilibrium with systems B and C individually, then systems B and C must be in thermal equilibrium with each other.

Step 2: Analyzing Statement (a)

Statement (a) suggests that system X is in thermal equilibrium with system Y, but not with system Z. It claims that systems Y and Z may be in thermal equilibrium. However, if X is in equilibrium with Y, Y can't simultaneously be in equilibrium with Z unless X is also in equilibrium with Z, according to the Zeroth Law. Hence, this statement is incorrect.

Step 3: Analyzing Statement (b)

In statement (b), system X is in thermal equilibrium with system Y, but not with Z. It states that Y and Z are not in thermal equilibrium. Given that Y is in equilibrium with X but not with Z, this condition adheres to the Zeroth Law of Thermodynamics. This statement is correct.

Step 4: Analyzing Statement (c)

Statement (c) proposes that system X is not in thermal equilibrium with systems Y or Z and asserts that Y and Z must be in equilibrium. There is no requirement for Y and Z to be in equilibrium just because X isn't with either, making this statement incorrect.

Step 5: Analyzing Statement (d)

Statement (d) states system X is not in thermal equilibrium with Y or Z and mentions Y and Z may be in thermal equilibrium with each other. Indeed, with no specific condition requiring Y and Z to be unequal, it is possible for Y and Z to be in equilibrium. Hence, this statement is correct.

Key Concepts

Thermal Equilibrium

Thermal equilibrium is a fundamental concept in thermodynamics, especially when discussing the principles laid out in the Zeroth Law of Thermodynamics. It defines a state in which two systems are at the same temperature and, as a result, no net heat flow occurs between them. This condition is essential for understanding how temperature makes systems balanced, ensuring energy does not spontaneously move from one object to another unless disrupted by a temperature difference.

The Zeroth Law states that if a system A is in thermal equilibrium with system B, and system B is in thermal equilibrium with system C, then A must also be in equilibrium with C. This transitive property suggests that all the systems involved will eventually reach a point where their temperatures are equal, given enough time, allowing them to achieve thermal balance. Understanding this fundamental concept is crucial for analyzing real-world situations involving heat and energy transfer, such as the readings on thermometers or the behavior of mixed substances.

System Analysis

System analysis in the context of thermal equilibrium involves examining the interactions between multiple systems or objects to determine their thermal relationships. Through a detailed analysis of systems, we can deduce relationships based on temperature and predict energy exchanges. When undertaking system analysis, it is vital to assess whether systems are in thermal equilibrium to determine the direction and nature of heat flow.

Analyzing situations like the ones presented in the exercise requires a meticulous evaluation of each system's thermal state. For example, if system X is in thermal equilibrium with system Y, this relationship implies specific characteristics of heat energy exchange or lack thereof. System analysis requires identifying such equilibrium conditions and validating them against the principles outlined by the Zeroth Law. It helps to establish whether assumptions about system interrelations are consistent with physical laws, guiding us to accurate conclusions.

NCERT Exemplar

The NCERT Exemplar problems are designed to challenge and deepen a student's understanding of thermodynamic concepts, including the Zeroth Law of Thermodynamics. These problems encourage learners to apply theoretical knowledge to practical examples, fostering a more intuitive grasp of how thermal equilibrium operates in different scenarios.

By engaging with exemplar problems, students enhance their ability to reason through complex thermodynamic situations. For instance, through consideration of various statements regarding the thermal relationships between systems like X, Y, and Z, learners acquire critical thinking and problem-solving skills. They learn to validate or refute conditions based on established thermodynamic laws. This approach not only strengthens their conceptual framework but also prepares them for advanced studies in physics, where precise and critical analysis is paramount.