Two systems, each composed of two particles represented by circles, have 20 J of total energy. Which system, A or B, has the greater entropy? Why?

Verified step by step guidance

Step 1: Understand the concept of entropy. Entropy is a measure of the number of possible configurations or microstates that a system can have. A system with more possible configurations has higher entropy.

Step 2: Consider the distribution of energy among the particles in each system. If one system has more ways to distribute the energy among its particles, it will have higher entropy.

Step 3: Analyze the possible energy distributions for each system. For example, if System A can distribute the energy in more ways than System B, then System A has higher entropy.

Step 4: Consider the number of particles and their possible energy states. More particles or more energy states typically lead to more possible configurations, increasing entropy.

Step 5: Compare the systems based on the above analysis. Determine which system has more possible configurations for distributing the 20 J of energy, and thus, which has greater entropy.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.

Video duration:

Was this helpful?

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Entropy

Entropy is a measure of the disorder or randomness in a system. In thermodynamics, it quantifies the number of ways a system can be arranged while maintaining the same energy level. Higher entropy indicates a greater number of possible microstates, leading to increased disorder. In the context of two systems with the same energy, the system with more possible arrangements of particles will have higher entropy.

Microstates and Macrostates

A macrostate is defined by macroscopic properties such as energy and temperature, while microstates refer to the specific arrangements of particles that correspond to a macrostate. The relationship between microstates and macrostates is crucial for understanding entropy; a macrostate with more microstates has higher entropy. Thus, when comparing two systems with the same total energy, the one with more microstates will exhibit greater entropy.

Energy Distribution

Energy distribution among particles affects the entropy of a system. When energy is distributed more evenly among particles, it allows for a greater number of microstates, thus increasing entropy. In the context of the question, if one system allows for more ways to distribute the total energy of 20 J among its particles, it will have higher entropy compared to the other system.

Recommended video:

Guided course

02:47

Velocity Distributions

Related Practice

Textbook Question

Which of these processes are nonspontaneous? Are the nonspontaneous processes impossible? a. a bike going up a hill b. a meteor falling to Earth c. obtaining hydrogen gas from liquid water d. a ball rolling down a hill

Textbook Question

Calculate the change in entropy that occurs in the system when 1.50 mol of diethyl ether (C₄H₁₀O) condenses from a gas to a liquid at its normal boiling point (34.6 °C). See Table 12.7 for heats of vaporization.

Textbook Question

Which of these processes is spontaneous? a. the combustion of natural gas b. the extraction of iron metal from iron ore c. a hot drink cooling to room temperature d. drawing heat energy from the ocean's surface to power a ship

Textbook Question

Calculate the change in entropy that occurs in the system when 1.50 mol of isopropyl alcohol (C₃H₈O) melts at its melting point (-89.5 °C). See Table 12.9 for heats of fusion.

Textbook Question

Two systems, each composed of three particles represented by circles, have 30 J of total energy. How many energetically equivalent ways can you distribute the particles in each system? Which system has greater entropy?