Equipartition, Specific Heats and Mean Free Path

Name: Equipartition, Specific Heats and Mean Free Path
Author: StemPy Lab

A molecule can move, turn and vibrate. Each way of storing energy gets the same share of it. From that one rule we find the specific heats of gases, of mixtures, of solids and of water. Then we ask how far a molecule travels before it hits another one.

3 lessons, about 1 h 30 min3 simulations12 problems6 practice questionsPython in every lesson

Created by StemPy Lab

Course outline (3 lessons)

Lesson 1about 30 min
Degrees of freedom and equipartition
A molecule can store energy by moving, by turning and by vibrating. Each independent squared term in its energy is a degree of freedom. The law of equipartition says each one gets $\tfrac12 k_BT$ on average, so one molecule has $\tfrac{f}{2}k_BT$ and one mole has $U = \tfrac{f}{2}RT$ .
1 simulation2 practice questions1 Python program4 problems1 Python lab
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Lesson 2about 30 min
Specific heat capacities of gases and solids
From $U = \tfrac{f}{2}nRT$ , the molar heat capacity at constant volume is $C_v = \tfrac{f}{2}R$ , and $\gamma = 1 + \tfrac{2}{f}$ . A mixture has a mole-weighted $C_v$ . A solid has $C = 3R$ (Dulong and Petit), and water about $9R$ . At low temperatures the measured values fall below these, which classical physics cannot explain.
1 simulation2 practice questions1 Python program4 problems1 Python lab
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Lesson 3about 30 min
Mean free path
A gas molecule moves in a straight line until it hits another, then changes direction. The average distance between two collisions is the mean free path, $\lambda = \dfrac{1}{\sqrt{2}\,\pi d^2 n}$ . Using $n = p/k_BT$ , it grows with the temperature and falls with the pressure.
1 simulation2 practice questions1 Python program4 problems1 Python lab1 question set1 note
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Equipartition and Specific Heats: Mock Exam

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More onHeat & Thermodynamics › Kinetic Theory of Gases Heat & Thermodynamics › Thermodynamic Processes and Specific Heats of Gases

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Equipartition, Specific Heats and Mean Free Path

Course outline (3 lessons)

Degrees of freedom and equipartition

Specific heat capacities of gases and solids

Mean free path

Test Your Learning

Your teacher

Discussion (0)