## The puddle

• differentials
• assignment Potential energy of gas in gravitational field

assignment Homework

##### Potential energy of gas in gravitational field
Potential energy Heat capacity Thermal and Statistical Physics 2020 Consider a column of atoms each of mass $M$ at temperature $T$ in a uniform gravitational field $g$. Find the thermal average potential energy per atom. The thermal average kinetic energy is independent of height. Find the total heat capacity per atom. The total heat capacity is the sum of contributions from the kinetic energy and from the potential energy. Take the zero of the gravitational energy at the bottom $h=0$ of the column. Integrate from $h=0$ to $h=\infty$. You may assume the gas is ideal.
• group Optical depth of atmosphere

group Small Group Activity

30 min.

##### Optical depth of atmosphere
Contemporary Challenges 2022 (4 years) In this activity students estimate the optical depth of the atmosphere at the infrared wavelength where carbon dioxide has peak absorption.
• assignment Differentials of Two Variables

assignment Homework

##### Differentials of Two Variables
Static Fields 2022 (8 years) Find the total differential of the following functions:
1. $y=3u^2 + 4\cos 3v$
2. $y=3uv$
3. $y=3u^2\cos wv$
4. $y=u\cos(3v^2-2)$
• assignment Zapping With d 1

assignment Homework

##### Zapping With d 1
Energy and Entropy 2021 (2 years)

Find the differential of each of the following expressions; zap each of the following with $d$:

1. $f=3x-5z^2+2xy$

2. $g=\frac{c^{1/2}b}{a^2}$

3. $h=\sin^2(\omega t)$

4. $j=a^x$

5. $k=5 \tan\left(\ln{\left(\frac{V_1}{V_2}\right)}\right)$

• face Energy and Entropy review

face Lecture

5 min.

##### Energy and Entropy review
Thermal and Statistical Physics 2020 (3 years)

This very quick lecture reviews the content taught in Energy and Entropy, and is the first content in Thermal and Statistical Physics.
• group Gravitational Potential Energy

group Small Group Activity

60 min.

##### Gravitational Potential Energy

Students examine a plastic “surface” graph of the gravitational potential energy of an Earth-satellite system to explore the properties of gravitational potential energy for a spherically symmetric system.
• Static Fields 2022 (5 years) The depth of a puddle in millimeters is given by $h=\frac{1}{10} \bigl(1+\sin(\pi xy)\bigr)$ Your path through the puddle is given by $x=3t \qquad y=4t$ and your current position is $x=3$, $y=4$, with $x$ and $y$ also in millimeters, and $t$ in seconds.
1. At your current position, how fast is the depth of water through which you are walking changing per unit time?
2. At your current position, how fast is the depth of water through which you are walking changing per unit distance?
3. FOOD FOR THOUGHT (optional)
There is a walkway over the puddle at $x=10$. At your current position, how fast is the depth of water through which you are walking changing per unit distance towards the walkway.