Problem 26 - Chemistry The Central Science In Si Units

Question

(a) Does the entropy of the surroundings increase for spontaneous processes? (b) In a particular spontaneous process the entropy of the system decreases. What can you conclude about the sign and magnitude of \(\Delta S_{\text {surr }} ?\) (c) During a certain reversible process, the surroundings undergo an entropy change, \(\Delta S_{\text {surr }}=-78 \mathrm{~J} / \mathrm{K} .\) What is the entropy change of the system for this process?

Step-by-Step Solution

Answer

(a) Yes, entropy of the surroundings generally increases for spontaneous processes. (b) \(\Delta S_{\text{surr}} > 0\) and \(\Delta S_{\text{surr}} > -\Delta S_{\text{sys}}\). (c) \(\Delta S_{\text{sys}} = 78 \text{ J/K}\).

Step 1: Understanding Entropy and Spontaneous Processes

For any spontaneous process, the total entropy change, which is the sum of the entropy change of the system and surroundings, must be positive. This is because the Second Law of Thermodynamics states that the entropy of the universe always increases in spontaneous processes.

Step 1: Analyzing Entropy of the Surroundings

For spontaneous processes, the entropy of the surroundings can either increase or decrease, depending on the process, but the total entropy of the universe must increase. So, generally, the entropy of the surroundings will more often increase, contributing to the overall positive change in entropy of the universe.

Step 2: Analyzing the Given Spontaneous Process

In the given spontaneous process, it is stated that the entropy of the system decreases. Therefore, to satisfy the Second Law of Thermodynamics, the change in entropy of the surroundings, \(\Delta S_{\text{surr}}\), must be positive and greater in magnitude than the negative change in entropy of the system, \(-\Delta S_{\text{sys}}\), to make the total entropy change positive.

Step 3: Determining Entropy Change in a Reversible Process

For a reversible process, the total change in entropy is zero, meaning \(\Delta S_{\text{sys}} + \Delta S_{\text{surr}} = 0\). Given that \(\Delta S_{\text{surr}} = -78 \text{ J/K}\), we can determine that \(\Delta S_{\text{sys}} = 78 \text{ J/K}\), so that the sum of the entropy changes equals zero.

Key Concepts

Second Law of Thermodynamics

The Second Law of Thermodynamics is a fundamental principle that describes the direction of processes in nature. It states that the total entropy of the universe, which is the sum of the entropy changes in the system and its surroundings, always tends to increase over time for any spontaneous process.

This law implies some crucial aspects about natural processes:

• Entropy, often considered a measure of disorder, naturally increases, which means systems tend to evolve toward more disordered states.
• When a process occurs spontaneously, the combined entropy of the system and surroundings must show a net increase.
• The Second Law helps us understand why certain processes, like heat flowing from a hot object to a cold one, occur naturally, while the reverse requires external intervention.

A key outcome of this law is that it sets the direction of energy transformations and ensures that energy transfer has an inherent inefficiency due to increasing entropy. It's a critical guideline in determining how processes can be conducted and how systems tend to reach equilibrium.

Spontaneous Processes

Spontaneous processes are those that occur naturally without the need for external energy input. These processes are driven by the tendency to increase the total entropy of the universe according to the Second Law of Thermodynamics.

There are a few important points to remember about spontaneous processes:

• The entropy change of the system may be positive or negative, but the total entropy change of the universe (system plus surroundings) must be positive.
• If a process is spontaneous and the system's entropy decreases, the surroundings' entropy must increase by a greater amount to ensure a net positive change in entropy.
• Spontaneous processes are not necessarily quick processes; some spontaneous reactions can be slow without contradicting the laws of thermodynamics.

Understanding why processes are spontaneous helps in predicting the behavior and equilibrium of systems, and allows scientists and engineers to optimize processes by manipulating conditions to favor desirable outcomes.

Reversible Processes

Reversible processes are idealized processes that occur extremely slowly and can be undone by infinitesimal changes in a system's properties. In real life, no process is perfectly reversible, but understanding this concept provides a crucial benchmark for efficiency.

The key characteristics of reversible processes include:

• The total change in entropy for a reversible process is zero, meaning that the entropy change in the system is exactly balanced by the entropy change in the surroundings.
• These processes are theoretical constructs that assume no dissipation of energy as waste heat or any increase in disorder.
• Reversible processes require equilibrium at each stage of the transformation, making them infinitely slow and thus not practically achievable.

By examining reversible processes, we can better understand limits of efficiency in engines and refrigerators, as real systems can only aspire to approach these limits. It highlights fundamental constraints in energy conversion processes, aiding in the development of more efficient technologies.