Question

The entropy of a system can: a. never decrease. b. decrease when the entropy of the surroundings increases by at least as much. c. decrease when the system is isolated and the process is irreversible. d. decrease during an adiabatic reversible process.

Short answer

Option b is correct. The entropy of a system can decrease if the entropy of the surroundings increases by at least as much, ensuring the total entropy remains non-decreasing.

Step-by-step solution

Understand the second law of thermodynamics

The second law of thermodynamics states that for any spontaneous process, the total entropy of a system and its surroundings always increases. An isolated system will never experience a decrease in its entropy.

Analyze option a

Option a states that the entropy of a system can never decrease. This statement is too restrictive, as there are scenarios where a system’s entropy can decrease while considering the total entropy of the system and surroundings together.

Analyze option b

Option b states that the entropy of a system can decrease when the entropy of the surroundings increases by at least as much. This aligns with the second law of thermodynamics because the total entropy change (system + surroundings) would still be positive or zero.

Analyze option c

Option c states that the entropy of a system can decrease when the system is isolated and the process is irreversible. For an isolated system, the entropy can never decrease, so this statement is false.

Analyze option d

Option d states that the entropy of a system can decrease during an adiabatic reversible process. In a reversible process, the total entropy change is zero, but the system’s entropy may decrease if the surroundings’ entropy increases by the same amount (adiabatic refers to no heat exchange with surroundings).

Conclusion

Review the options to determine which is consistent with the second law of thermodynamics. Find that option b is the only correct statement.

Key concepts

entropy

Entropy is a measure of the disorder or randomness in a system. According to the second law of thermodynamics, the total entropy of a system and its surroundings always tends to increase in a spontaneous process.
For a deeper understanding of entropy, think of it as a way to quantify the number of microscopic configurations that a system can have. When a process increases disorder, entropy increases.
Examples include:

• Melting of ice: Solid water (ice) has lower entropy because its molecules are orderly. When it melts, it turns into liquid water, where molecules move more freely, increasing entropy.
• Mixing two gases: Unmixed gases have lower entropy. Upon mixing, the mixture has higher entropy as the molecules are more randomly distributed.

spontaneous process

A spontaneous process is any physical or chemical change that occurs naturally without needing external energy once it starts. These processes always result in an overall increase in entropy (the total entropy of the system and its surroundings).
In simpler terms, a spontaneous process is one that happens on its own, like ice melting on a warm day or iron rusting when exposed to moisture.
Key points to note:

• Spontaneity doesn't necessarily mean the process is fast—some spontaneous processes can be slow, such as the rusting of iron.
• A spontaneous process must result in a positive total change in entropy.

adiabatic process

An adiabatic process is one in which no heat is transferred into or out of the system. This can happen when the system is perfectly insulated.
Adiabatic processes come in two main types: reversible and irreversible.

• In a reversible adiabatic process, the entropy change is zero, since the system can return to its original state without any net change in entropy.
• In an irreversible adiabatic process, the entropy of the system increases because the process generates entropy.

An example of an adiabatic process is the rapid compression of a gas in an insulated cylinder, where no heat is exchanged with the surroundings.

isolated system

An isolated system is one that does not exchange matter or energy with its surroundings. For such systems, the total energy and matter remain constant.
According to the second law of thermodynamics, the entropy of an isolated system can never decrease. Over time, the entropy will either increase or remain constant if the system is in equilibrium.
Points to remember:

• Entropy of an isolated system tends to a maximum state over time, as it favors disorder.
• Since no external interactions affect an isolated system, its evolution is completely governed by its internal properties.

A typical example of an isolated system in thermodynamics would be an insulated container with gas that neither absorbs nor releases heat or matter.