Question

Taken together, a certain closed system and its surroundings make up an isolated system. Answer the following true or false. If false, explain why. (a) No process is allowed in which the entropies of both the system and the surroundings increase. (b) During a process, the entropy of the system might decrease, while the entropy of the surroundings increases, and conversely. (c) No process is allowed in which the entropies of both the system and the surroundings remain unchanged. (d) A process can occur in which the entropies of both the system and the surroundings decrease.

Short answer

a: False, b: True, c: False, d: False

Step-by-step solution

Understanding the problem

The problem involves determining the truth of statements about entropy changes in an isolated system. An isolated system means no exchange of energy or matter with the surroundings.

Analyze statement (a)

Statement (a) says no process is allowed where both the system's and the surroundings' entropies increase. In an isolated system, total entropy can stay the same or increase, but cannot decrease. Since both increasing does not violate this, the statement is false.

Analyze statement (b)

Statement (b) suggests that entropy of the system might decrease while that of the surroundings increases, and conversely. This is true because as long as the total entropy increases or remains the same, individual parts can change in opposite directions.

Analyze statement (c)

Statement (c) suggests no process is allowed where both system and surroundings' entropies remain unchanged. This is false because reversible processes exist where the total entropy does not change.

Analyze statement (d)

Statement (d) claims a process can occur where both system and surroundings' entropies decrease. This is false because in an isolated system, the total entropy cannot decrease.

Key concepts

Understanding Entropy

Entropy is a fundamental concept in thermodynamics. It's a measure of disorder or randomness in a system. The second law of thermodynamics states that in an isolated system, the total entropy can never decrease over time; it either increases or remains constant in a reversible process. This means that energy will always spread out or become more disordered unless work is done to keep it organized.

For example, if you leave an ice cube in a warm room, it will melt. The molecules in the ice, initially structured, will move around more freely in the water, increasing the system's entropy.

When thinking about entropy changes in processes, remember:

• The total entropy of an isolated system never decreases.
• In real-world processes, the entropy usually increases.

A practical tip is to visualize entropy as a measure of energy dispersal. The more spread out the energy, the higher the entropy.

Isolated Systems

An isolated system is a special type of closed system. It does not exchange energy or matter with its surroundings. Because of this, it is often used to study the laws of thermodynamics in a simplified context. The entire universe is considered an isolated system because there is nothing outside of it to exchange energy or matter with.

In isolated systems, a few important points hold:

• No matter (mass) or energy can enter or leave the system.
• The total energy of the system remains constant.
• The total entropy of the system will either increase or stay the same, but never decrease.

These points help us understand why processes in isolated systems behave in predictable ways.

For instance, consider a perfectly insulated container with a hot and a cold object inside. Over time, heat from the hot object will transfer to the cold one until both reach the same temperature. The system has moved to a more probable state of uniform temperature, increasing the total entropy.

Basic Thermodynamics Principles

Thermodynamics is the study of energy, heat, work, and how they interrelate. It is governed by four basic laws which are crucial for understanding physical processes:

1. The Zeroth Law of Thermodynamics states that if two systems are in thermal equilibrium with a third one, they are in thermal equilibrium with each other.

2. The First Law of Thermodynamics, also known as the Law of Energy Conservation, states that energy cannot be created or destroyed, only transferred or converted from one form to another. The equation to describe this is: \[ \text{ΔU} = Q - W \] where \text{ΔU} is the change in internal energy, \text{Q} is the heat added to the system, and \text{W} is the work done by the system.

3. The Second Law of Thermodynamics states that the entropy of an isolated system always increases over time. It implies that natural processes have a preferred direction of progression, often toward more disorder.

4. The Third Law of Thermodynamics states that the entropy of a perfect crystal at absolute zero is exactly zero.

These laws help explain how energy moves and changes form, making them crucial for understanding isolated systems and entropy changes. For practical use, remember that increasing entropy is like energy becoming more scattered and hard to use without inputting extra work to organize it again.