Question

Indicate whether each statement is true or false. (a) The second law of thermodynamics says that entropy is conserved. (b) If the entropy of the system increases during a reversible process, the entropy change of the surroundings must decrease by the same amount. (c) In a certain spontaneous process the system undergoes an entropy change of \(4.2 \mathrm{J} / \mathrm{K} ;\) therefore, the entropy change of the surroundings must be \(-4.2 \mathrm{J} / \mathrm{K}\)

Short answer

(a) False - The second law of thermodynamics states that the entropy of an isolated system never decreases; it either increases or remains the same during a spontaneous process, meaning that entropy is not conserved. (b) True - In a reversible process, if the entropy of the system increases, the entropy of the surroundings must decrease by the same amount for the total change to be zero. (c) False - In a spontaneous process, we cannot say that the entropy change of the surroundings is necessarily -4.2 J/K, as the total change must be positive for the process to be spontaneous.

Step-by-step solution

(a) Entropy Conservation

The second law of thermodynamics states that the entropy of an isolated system never decreases; it either increases or remains the same during a spontaneous process. This means that entropy is not conserved. Therefore, the statement is false.

(b) Entropy change in reversible process

In a reversible process, the total entropy change in a system and its surroundings is zero. This means that if the entropy of the system increases, the entropy of the surroundings must decrease by the same amount for the total change to be zero. Therefore, the statement is true.

(c) Entropy change in spontaneous process

In a spontaneous process, the total entropy change in the system and its surroundings is positive. The statement mentions that the entropy change of the system is 4.2 J/K, which means there is an increase in the system's entropy. However, we cannot say that the entropy change of the surroundings is necessarily -4.2 J/K, as the total change must be positive for the process to be spontaneous. Therefore, the statement is false.

Key concepts

Second Law of Thermodynamics

Imagine the universe as a movie that plays in one direction and never goes backward. That's how the second law of thermodynamics works. This law is one of the fundamental concepts in physics and chemistry. It states that the entropy, or the measure of disorder, of an isolated system will never decrease. It can either increase or remain constant over time, particularly during spontaneous processes.
Entropy is a tricky concept. When we say it never decreases, what we mean is that the universe prefers disorder. Think of it like a messy room—it never gets tidier on its own!

• Entropy is always increasing or staying the same.
• Entropy means chaos or disorder.
• This is a one-way street; once things get messy, they rarely clean themselves up spontaneously.

So, whenever you think about the universe doing its thing, it's really just entropy finding cozy places to hide in complete chaos!

Reversible Process

A reversible process is like walking a tightrope with perfect balance. In real life, such balansing acts are often impossible to achieve exactly, but they are a useful way to understand ideal processes. In a reversible process, everything is in perfect equilibrium. This means that any small change in the process can be reversed, bringing the system back to its original state.
Remember, reversible means that the total entropy change is zero.

• If the system's entropy goes up, the entropy of the surroundings goes down by the same amount.
• When you sum up the entropy changes of the system and the surroundings, the net effect is zero.
• This perfect balance is a theoretical concept that's rarely achieved in reality due to the presence of friction, heat loss, or other irreversibilities.

Reversible processes are more like dreams than reality, but they give us a useful way to understand how systems ideally work.

Spontaneous Process

A spontaneous process is like a snowball rolling downhill; it picks up speed and can't stop on its own. In scientific terms, it means a process that occurs naturally without needing any external energy once it has started. Spontaneous processes are characterized by a positive overall change in entropy, meaning the disorder in the combined system and surroundings is increasing.

• The entropy of the system might increase or decrease, but the combined entropy of the system and surroundings must increase.
• Energy spreads out without input—imagine a drop of dye diffusing in water.
• It is about balancing both the entropy of the system and the surroundings.

So, even if the system's entropy increases by a certain value, like 4.2 J/K, the surroundings might contribute additional entropy that leads to an overall increase. Remember, in the universe, spontaneous is synonymous with natural and inevitable chaos!