Problem 22 - Chemistry The Central Science In Si Units

Question

Indicate whether each statement is true or false. (a) The entropy of the universe increases for any spontaneous process. (b) The entropy change of the system is equal and opposite that of the surroundings for any irreversible process. (c) The entropy of the system must increase in any spontaneous process. (d) The entropy change for an isothermal process depends on both the absolute temperature and the amount of heat reversibly transferred.

Step-by-Step Solution

Answer

(a) True, (b) False, (c) False, (d) True.

Step 1: Analyze Statement (a)

The statement claims that the entropy of the universe increases for any spontaneous process. According to the second law of thermodynamics, for any spontaneous process, the total entropy, which is the sum of the entropy changes of the system and its surroundings, must increase. Therefore, statement (a) is true.

Step 2: Analyze Statement (b)

This statement suggests that the entropy change of the system is equal and opposite that of the surroundings for any irreversible process. In irreversible processes, the total entropy (system plus surroundings) increases, but the entropy change of the system is not equal and opposite to that of the surroundings; rather, the universe experiences an overall increase in entropy. Thus, statement (b) is false.

Step 3: Analyze Statement (c)

The statement asserts that the entropy of the system must increase in any spontaneous process. While a spontaneous process leads to an increase in the entropy of the universe, the system alone may not always have an entropy increase. It is possible for the system's entropy to decrease if the surroundings' entropy increases more. Therefore, statement (c) is false.

Step 4: Analyze Statement (d)

The statement discusses the entropy change for an isothermal process, indicating it depends on both absolute temperature and heat reversibly transferred. For isothermal processes, the entropy change \( \Delta S \) is given by \( \Delta S = \frac{q_{rev}}{T} \), where \( q_{rev} \) is the reversible heat transfer and \( T \) is the absolute temperature. Both the temperature and the reversible heat are factors. Thus, statement (d) is true.

Key Concepts

Second Law of Thermodynamics

The second law of thermodynamics provides us with a very intriguing rule of nature. It essentially tells us that energy has a direction of flow in physical processes. This law states that for any spontaneous process, the total entropy of the universe increases. When we talk about the universe here, we mean both the system (the part of the universe we're focused on) and its surroundings (everything else).

It’s fascinating to note that this means processes naturally occur in the direction that increases the universe's entropy. So, melting ice in a warm room is a spontaneous process because it results in increased entropy.

• Spontaneous processes: Happen by themselves without needing extra energy.
• Increased entropy: Reflects disorder or randomness.

As such, according to the second law, the universe tends to move towards greater disorder and randomness.

Entropy

Entropy is a measure of randomness or disorder within a system. Imagine cleaning your room; when it's tidy, it has low entropy - everything's in place. But when it’s messy, it has high entropy - there's more randomness in item positions.

Entropy tells us about the direction of a process. For example, heat naturally flows from hot objects to cold ones, increasing entropy.

• Measure of disorder: A quantitative way to assess the degree of randomness.
• Natural processes increase entropy: Systems tend to evolve from ordered to disordered states.

Importantly, while the universe's total entropy must increase, individual systems might experience a decrease if their surroundings' entropy increases even more.

Spontaneous Processes

Spontaneous processes occur without requiring energy input from outside the system. These processes tend to lead to higher entropy in the universe. For example, rust forming on iron does so spontaneously and increases overall entropy.

A key point is that just because a process is spontaneous doesn’t mean it happens quickly. Some processes can take a long time to occur even though they are spontaneous.

• Occur without external energy: They happen on their own.
• Increase overall entropy: They contribute to greater disorder in the universe.

It’s a natural tendency for spontaneous processes to lead to a more disordered or random state.

Irreversible Processes

Irreversible processes are those that cannot be undone by reversing the conditions. These processes contribute to an increase in the total entropy of the universe.

Imagine mixing cream into coffee; you can’t easily take the cream back out. That's irreversible, and during such a process, the entropy typically increases.

• Cannot be reversed perfectly: Once completed, returning to the original state is impossible.
• Increase in total entropy: These processes increase the disorder of the universe.

In irreversible processes, unlike reversible ones, entropy changes are not simply the opposite between the system and surroundings; rather, the whole system-surroundings setup experiences greater entropy.