Problem 25 - Chemistry: The Central Science in SI Units, Global Edition

Question

Indicate whether each statement is true or false. (a) The second law of thermodynamics says that entropy can only be produced but cannot not be destroyed. (b) In a certain process the entropy of the system changes by \(1.2 \mathrm{~J} / \mathrm{K}\) (increase) and the entropy of the surroundings changes by \(-1.2 \mathrm{~J} / \mathrm{K}\) (decrease). Thus, this process must be spontaneous. (c) In a certain process the entropy of the system changes by \(1.3 \mathrm{~J} / \mathrm{K}\) (increase) and the entropy of the surroundings changes by \(-1.2 \mathrm{~J} / \mathrm{K}\) (decrease). Thus, this process must be reversible.

Step-by-Step Solution

Answer

(a) True (b) False (c) False

Step 1: Statement (a)

The second law of thermodynamics states that the total entropy in a closed system can only increase but cannot decrease. In other words, entropy can be created but not destroyed. So, the statement is true.

Step 2: Statement (b)

To determine if this process is spontaneous, we need to consider the overall entropy change in the system and the surroundings. If the total entropy change is positive, the process is spontaneous according to the second law of thermodynamics. Total entropy change is the sum of the entropy change of the system and the surroundings, which is: \(1.2 J/K + (-1.2 J/K) = 0 J/K\). Since the total entropy change is zero, the process is not spontaneous, and the statement is false.

Step 3: Statement (c)

To determine if this process is reversible, we can again consider the overall entropy change in the system and the surroundings. For a process to be reversible, the total entropy change must be zero. In this case, the total entropy change is: \(1.3 J/K + (-1.2 J/K) = 0.1 J/K\), which is not zero. Thus, the process is not reversible, and the statement is false.

Key Concepts

Entropy

Entropy is a measure of disorder or randomness in a system. It is a fundamental concept in thermodynamics, reflecting how energy is distributed within a system. A higher entropy means greater disorder.
Imagine a clean room versus a messy one; the messy room is less ordered, similar to a system with high entropy. Entropy can help predict the direction of energy flow.
A key insight is that in isolated systems, entropy tends to increase over time. This is because systems naturally progress towards more disordered states. However, in specific scenarios, such as when energy is added to the system, entropy may decrease locally, though overall universal entropy rises.
Entropy's increase is crucial in understanding the feasibility of processes, signifying how certain transformations occur naturally.

Second Law of Thermodynamics

The second law of thermodynamics is a cornerstone of understanding natural processes. It states that in any closed system, the total entropy can never decrease over time.
Rather, it can only stay constant or go up. This implies that energy transformations are inherently inefficient. Some energy always spreads out into less useful forms.
The law helps us understand why certain processes happen spontaneously. For example, heat will flow from a hot object to a cold one, but not the reverse, because this increases total entropy.
This principle also explains the inevitable decline of order or usable energy in an isolated system, guiding our understanding of processes from ice melting to chemical reactions.

Spontaneity

Spontaneity in thermodynamics refers to the natural occurrence of a process without external influence. A process is spontaneous if it results in an increase in total entropy.
Think of it as a naturally occurring transformation tending toward more disorder. For instance, sugar dissolving in water is spontaneous because it happens without energy input, driven by an increase in entropy.
Analyzing spontaneity in a given scenario involves evaluating the combined entropy change of the system and its surroundings. If the total change is positive, the process is spontaneous.
However, if there is no change in entropy, the process is at equilibrium and not spontaneous. Therefore, total entropy change provides critical insight into the nature of thermodynamic processes.

Reversible Processes

Reversible processes are idealized concepts in thermodynamics where a system undergoes a change in such a way that both the system and the surroundings can be returned to their original states without any net change in entropy.
In reality, perfectly reversible processes are hypothetical because they require an infinitely slow progression to maintain equilibrium throughout.
In a reversible process, the total change in entropy is zero. This contrasts with typical, irreversible processes, where entropy increases.
Understanding reversible processes is important because they establish the upper limit of efficiency for engines and other systems. While no true reversible processes exist, they remain a useful benchmark in thermodynamics.