## What is Temperature?

This video is part of the ** Equilibrium** video series.

### Video Summary

This video motivates the statistical mechanics approach through material structure and behavior. Entropy is introduced as a natural variable whose derivative with respect to energy is zero when the number of microstates is maximized. This derivative is identified as being the reciprocal of temperature, and Boltzmann’s constant is explained.

### Learning Objectives

After watching this video students will be able to explain how the definition of temperature arises as a derivative of entropy with respect to energy.

### Student Experience

It is highly recommended that the video is paused when prompted so that students are able to attempt the activities on their own and then check their solutions against the video.

During the video, students will:

- Identify how to find the energy states of box 1 and box 2 that maximizes the number of microstates with those energies.
- Differentiate the expression for the number of microstates with respect to energy that corresponds to fixed energy states of E1 for box 1 and E-E1 for box 2.
- Identify the physical quantity that best represents the derivative of entropy with respect to energy with fixed volume and number by considering properties of thermal equilibrium.