# Heat and Temperature

## Prerequisites

Before entering this lesson, students should have:

• Some familiarity with thermodynamic terms (i.e. latent heat of fusion, heat capacity, specific heat, entropy, etc.).
• An ability to integrate and differentiate.
• Basic knowledge on how power relates to energy and on how to find the power dissipated in a resistor.

## In-class Content

### Lab: Ice Calorimetry Lab

Lab Highlights

1. This integrated laboratory activity is designed to help students understand heat, heat capacity and entropy.
2. Students use a water proof resistor to heat ice water while measuring the temperature.
3. In the lab write-up, students analyze their data to find heat capacity, latent heat, and changes in entropy.

### Lecture: Dulong and Petit Rule (5 minutes)

• Briefly introduce the rule of Dulong and Petit: the specific heat multiplied by the atomic weight of all substances should be approximately equal
• Emphasize that this is only a general rule or approximation
• This topic is often skipped and is not necessary for the rest of the curriculum, but does tie in quite nicely to the Ice Calorimetry Lab below.
##### Lecture notes from Dr. Roundy's 2014 course website:

In 1819, shortly after Dalton had introduced the concept of atomic weight in 1808, Dulong and Petit observed that if they measured the specific heat per unit mass of a variety of solids, and divided by the atomic weights of those solids, the resulting per-atom specific heat was essentially constant. This is the Dulong-Petit law, although we have since given a name to that constant, which is $3R$ or $3k_B$, depending on whether the relative atomic mass (atomic weight) or the absolute atomic mass is used. This law isn't precisely true, and isn't always true, and is never true at low temperatures. But it captures some physics that we will later call the equipartition theorem. We will write Dulong-Petit's law as: $$C_p=3Nk_B$$ where $N$ is the total number of atoms.

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