Problem 48 - 43 Years JEE ADVANCED (1978-2020) + JEE MAIN Chapterwise & Topicwise Solved Papers Chemistry

Question

Statement - 1 : There is a natural asymmetry between converting work to heat and converting heat to work. Statement - \(2:\) No process is possible in which the sole result is the absorption of heat form a reservoir and its complete conversion into work. [2008S] (a) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1. (b) Statement- 1 is True, Statement-2 is True; Statement- 2 is NOT a correct explanation for Statement-1 (c) Statement- 1 is True, Statement- 2 is False (d) Statement- 1 is False, Statement- 2 is True

Step-by-Step Solution

Answer

(a) Both statements are true; Statement 2 explains Statement 1.

Step 1: Understanding Statement 1

Statement 1 discusses the natural asymmetry in energy conversion between work and heat. According to the second law of thermodynamics, it's easier to convert work into heat than to completely convert heat into work. Therefore, this statement reflects a basic principle of thermodynamics and is true.

Step 2: Analyzing Statement 2

Statement 2 asserts that no process can exist where heat is completely converted into work without any other change. This is a reflection of the Kelvin-Planck statement of the second law of thermodynamics, which affirms the impossibility of 100% conversion of heat into work. This statement is indeed true.

Step 3: Evaluating Explanation Relationship

Statement 2 provides a specific formulation of the second law of thermodynamics, which is a direct reflection of the idea in Statement 1 about conversion asymmetry. Therefore, Statement 2 indeed explains why Statement 1 holds true.

Key Concepts

Heat to Work Conversion

One of the central ideas in thermodynamics is the conversion of heat energy into work. This transformation forms the basis of many machines and engines, like those in cars and power plants. However, achieving complete heat to work conversion is more challenging than it may seem. According to the second law of thermodynamics, this process is naturally limited by inefficiencies and energy dissipation.

When heat is converted to work, not all the heat can turn into useful work. Some energy is inevitably lost to the surroundings, usually as waste heat. This reflects the law that no engine can be 100% efficient. To picture this, imagine a steam engine: it takes heat from burning coal, converts some into motion (work), and the rest escapes as smoke or waste heat to the environment.

Here are key points about heat to work conversion:

• Involves transforming thermal energy into mechanical energy.
• Cannot achieve 100% efficiency due to inherent losses.
• Relates to the concept that heat will always tend to disperse, making full conversion impossible.

Understanding these limitations is crucial to designing efficient machines.

Kelvin-Planck Statement

The Kelvin-Planck statement provides a formal declaration of one aspect of the second law of thermodynamics. It specifically talks about the impossibility of totally converting heat from a single reservoir into work through any process.

This means, even with the most advanced technology, an engine cannot extract heat from a high-temperature source and entirely turn it into work without discharging any energy to a cooler area. This principle ties closely with the fact that energy processes naturally flow from high-temperature zones to low, ensuring some energy loss.

To break it down further:

• The concept implies a fundamental efficiency limit in all thermal machines.
• It is a major reason why perpetual motion machines of the second kind, which claim 100% efficiency, are impossible.
• Invokes the need for a heat sink to dispose of unrecoverable energy in the cycle.

The Kelvin-Planck statement underscores the very foundation of all heat engine analysis.

Energy Conversion Asymmetry

The asymmetry in energy conversion between work to heat and heat to work is a foundational concept in thermodynamics. It highlights that converting work entirely into heat is straightforward and achievable, but reversing this process entirely is not. This asymmetry arises from the nature of energy transactions defined by the second law of thermodynamics. While you can easily rub your hands together to produce heat (work to heat conversion), trying to completely convert that heat back into work without any loss is impractical.

Key considerations include:

• Work converting to heat is a naturally one-way street, always successful.
• Heat converting to work always involves losses and inefficiency.
• Reflects the universal tendency towards increased entropy or disorder.

This asymmetry shows why machines are always more effective at generating heat than harnessing it as work.