Introduction to entropy | Applications of thermodynamics | AP Chemistry | Khan Academy

TL;DR

Entropy measures the number of microstates available to a system, with more microstates corresponding to greater entropy. For an ideal gas, doubling the volume at constant temperature and moles, raising the temperature at constant volume and moles, or increasing the number of moles at constant temperature and volume increases the available microstates, making the entropy change positive. Read on to see how particle positions, velocities, and energies explain each result.

Transcript

• [Instructor] The concept of entropy is related to the idea of microstates. And to think about microstates, let's consider one mole of an ideal gas. So remember, n represents moles at a specific pressure, volume, and temperature. If the system of gas particles is at equilibrium, then the pressure, the volume, the number of moles, and the temperatu... Read More

Key Insights

• #️⃣ Entropy is a measure of the number of microstates in a system and represents the amount of disorder or randomness.
• #️⃣ Increasing the number of microstates increases entropy, while decreasing it decreases entropy.
• #️⃣ Changes in volume, temperature, and the number of moles can all affect the number of microstates and, consequently, the entropy of a system.
• #️⃣ The equation by Boltzmann relates entropy to the number of microstates.

Questions & Answers

Q: What is entropy, and how is it related to microstates?

Entropy, symbolized by S, is related to the number of microstates available to a system. More available microstates mean greater entropy, while fewer microstates mean lower entropy.

Q: What is a microstate in thermodynamics?

A microstate is one specific configuration of all the particle positions and energies in a system. It can be pictured as a snapshot showing where the particles are and how they are moving at one moment.

Q: What equation relates entropy to the number of microstates?

The equation is S = k ln W. In this equation, S is entropy, k is Boltzmann's constant, and W is the number of microstates.

Q: Why can a gas change microscopically while appearing unchanged macroscopically?

Its pressure, volume, number of moles, and temperature can remain the same while its particles continually change positions and velocities. Each new configuration of particle positions and energies is a different microstate.

Q: How does doubling the volume of an ideal gas affect its entropy?

Doubling the volume from V1 to V2 = 2V1 gives the gas particles more possible positions. When temperature and the one-mole quantity remain constant, the number of microstates increases, so S2 is greater than S1 and the entropy change is positive.

Q: How does increasing temperature affect the entropy of an ideal gas?

Increasing temperature makes the particles move faster on average and produces a greater range of speeds and velocities. At constant volume and number of moles, this creates more possible energies and microstates, so entropy increases and the entropy change is positive.

Q: How does increasing the number of moles affect entropy?

Increasing the amount of ideal gas from one mole creates more possible particle positions, energies, and arrangements. If temperature and volume stay constant, the number of microstates and the entropy both increase.

Q: What do disorder, order, and energy dispersal mean in terms of microstates?

An increase in disorder or energy dispersal corresponds to an increase in the number of available microstates and therefore greater entropy. An increase in order or a decrease in dispersal corresponds to fewer available microstates and lower entropy.

Summary & Key Takeaways

• Entropy is a measure of the number of microstates in a system, representing the possible positions and energies of particles.

• An increase in the number of microstates leads to an increase in entropy, while a decrease in the number of microstates leads to a decrease in entropy.

• Changes in volume, temperature, number of moles, and intermolecular forces can all affect the number of microstates and, therefore, the entropy of a system.