Problem 1 - 43 Years JEE ADVANCED (1978-2020) + JEE MAIN Chapterwise & Topicwise Solved Papers Chemistry

Question

The true statement amongst the following is :(a) Both \(\Delta \mathrm{S}\) and \(\mathrm{S}\) are functions of temperature. (b) Both \(\mathrm{S}\) and \(\Delta \mathrm{S}\) are not functions of temperature. (c) \(\mathrm{S}\) is not a function of temperature but \(\Delta \mathrm{S}\) is a function of temperature. (d) \(\mathrm{S}\) is a function of temperature but \(\Delta \mathrm{S}\) is not a function of temperature.

Step-by-Step Solution

Answer

Option (a) is correct; both \( S \) and \( \Delta S \) depend on temperature.

Step 1: Understanding Entropy (S)

Entropy, denoted by \( S \), is a state function that depends on temperature. Entropy is the measure of randomness or disorder in a system, and it inherently varies with changes in temperature since it depends on the thermal energy distribution of the system.

Step 2: Understanding Change in Entropy (ΔS)

The change in entropy, denoted as \( \Delta S \), is the difference in entropy between two states. It is given by the equation \( \Delta S = S_{final} - S_{initial} \). Since \( S \) is a function of temperature, \( \Delta S \) too depends on the temperature changes between the two states, making it a function of temperature.

Step 3: Evaluating Options

Given the explanations for \( S \) and \( \Delta S \), we assess the options: - (a) Both \( \Delta \mathrm{S} \) and \( \mathrm{S} \) are functions of temperature: True.- (b) Both \( \mathrm{S} \) and \( \Delta \mathrm{S} \) are not functions of temperature: False.- (c) \( \mathrm{S} \) is not a function of temperature but \( \Delta \mathrm{S} \) is a function of temperature: False.- (d) \( \mathrm{S} \) is a function of temperature but \( \Delta \mathrm{S} \) is not a function of temperature: False.

Step 4: Conclusion

The correct answer is option (a) as both \( S \) and \( \Delta S \) are influenced by temperature changes, thus making them functions of temperature.

Key Concepts

Change in Entropy

When we talk about the change in entropy (\( \Delta S \)), we're referring to the difference in the entropy of a system between two states. Understanding this concept involves realizing that entropy is not a static quantity. Just like how the weather can change from sunny to cloudy, entropy measures the change in disorder or randomness within a system.Typically, we calculate the change in entropy using the formula:\[ \Delta S = S_{\text{final}} - S_{\text{initial}} \]This equation clearly shows that if the final entropy of a system is greater than the initial, \( \Delta S \) will be positive, indicating an increase in disorder. Why does this matter? Well, many natural processes involve changes in entropy. For example, when ice melts into water, the system's entropy increases because the orderly arrangement of the ice crystals becomes the more random water molecules. This change is essential because it highlights the direction of processes and energy flow in the universe. In essence, \( \Delta S \), the change in entropy, is pivotal in understanding the tendency of systems to evolve towards more probable (disordered) states.

State Function

Entropy, symbolized by \( S \), is what scientists call a state function. This means its value depends solely on the current state of the system and not on how it got there. Think about altitude as a state function: whether you climb a hill or take an elevator, your height above sea level only depends on your current altitude, not the path you took.This idea of a state function is crucial for entropy because it implies that when calculating changes in entropy, we simply need the initial and final states. The path the system took to transition between these states does not affect \( \Delta S \). This property makes thermodynamic calculations involving entropy much easier.As a result,

• We can focus on what changes in a system, represented by state functions, rather than how everything occurred step-by-step.
• This characteristic allows entropy to effectively predict the feasibility of processes and states.

Overall, perceiving entropy as a state function helps us simplify our view of the system's behavior.

Temperature Dependence

Entropy (\( S \)) and its change (\( \Delta S \)) are intricately linked to temperature, primarily because temperature is a measure of the thermal energy available in a system. Higher temperatures typically mean more thermal energy. This translates into increased molecular motion, leading to greater randomness or disorder—an increase in entropy.To visualize, imagine heating a pot of water. As the temperature rises, the water molecules move faster and become more disordered, raising the entropy. Therefore, both \( S \) and \( \Delta S \) can change with temperature alterations.It's important to note that this dependency means:

• Systems at different temperatures can display vastly different entropic properties, even if their composition remains constant.
• Predicting the behavior of systems exposed to temperature variations becomes complex but can be managed by understanding these relationships.

In short, through the bonds of temperature dependence, entropy offers crucial insights into how energy and matter interact under varying thermal conditions.