- Vaporization Heat
*assignment*Calculation of $\frac{dT}{dp}$ for water*assignment*Homework##### Calculation of \(\frac{dT}{dp}\) for water

Clausius-Clapeyron Thermal and Statistical Physics 2020 Calculate based on the Clausius-Clapeyron equation the value of \(\frac{dT}{dp}\) near \(p=1\text{atm}\) for the liquid-vapor equilibrium of water. The heat of vaporization at \(100^\circ\text{C}\) is \(2260\text{ J g}^{-1}\). Express the result in kelvin/atm.*group*Heat and Temperature of Water Vapor*group*Small Group Activity30 min.

##### Heat and Temperature of Water Vapor

In this introduction to heat capacity, students determine a derivative that indicates how much the internal energy changes as the temperature changes when volume is held constant.*assignment*Derivatives from Data (NIST)*assignment*Homework##### Derivatives from Data (NIST)

Energy and Entropy 2021 (2 years) Use the NIST web site “Thermophysical Properties of Fluid Systems” to answer the following questions. This site is an excellent resource for finding experimentally measured properties of fluids.- Find the partial derivatives \[\left(\frac{\partial {S}}{\partial {T}}\right)_{p}\] \[\left(\frac{\partial {S}}{\partial {T}}\right)_{V}\] where \(p\) is the pressure, \(V\) is the volume, \(S\) is the entropy, and \(T\) is the temperature. Please find these derivatives for one gram of methanol at one atmosphere of pressure and at room temperature.
- Why does it take only two variables to define the state?
- Why are the derivatives above different?
- What do the words isobaric, isothermal, and isochoric mean?

*group*Ideal Gas Model*group*Small Group Activity30 min.

##### Ideal Gas Model

Students consider whether the thermo surfaces reflect the properties of an ideal gas.*biotech*Microwave oven Ice Calorimetry Lab*biotech*Experiment60 min.

##### Microwave oven Ice Calorimetry Lab

Energy and Entropy 2021 (2 years)heat entropy water ice thermodynamics

In this remote-friendly activity, students use a microwave oven (and optionally a thermometer) to measure the latent heat of melting for water (and optionally the heat capacity). From these they compute changes in entropy. See also Ice Calorimetry Lab.*face*Phase transformations*face*Lecture120 min.

##### Phase transformations

Thermal and Statistical Physics 2020phase transformation Clausius-Clapeyron mean field theory thermodynamics

These lecture notes from the ninth week of Thermal and Statistical Physics cover phase transformations, the Clausius-Clapeyron relation, mean field theory and more. They include a number of small group activities.*group*``Squishability'' of Water Vapor (Contour Map)*group*Small Group Activity30 min.

##### “Squishability” of Water Vapor (Contour Map)

Students determine the “squishibility” (an extensive compressibility) by taking \(-\partial V/\partial P\) holding either temperature or entropy fixed.*assignment*Vapor pressure equation*assignment*Homework##### Vapor pressure equation

phase transformation Clausius-Clapeyron Thermal and Statistical Physics 2020 Consider a phase transformation between either solid or liquid and gas. Assume that the volume of the gas is*way*bigger than that of the liquid or solid, such that \(\Delta V \approx V_g\). Furthermore, assume that the ideal gas law applies to the gas phase.**Note: this problem is solved in the textbook, in the section on the Clausius-Clapeyron equation.**Solve for \(\frac{dp}{dT}\) in terms of the pressure of the vapor and the latent heat \(L\) and the temperature.

Assume further that the latent heat is roughly independent of temperature. Integrate to find the vapor pressure itself as a function of temperature (and of course, the latent heat).

*group*Changes in Internal Energy (Remote)*group*Small Group Activity30 min.

##### Changes in Internal Energy (Remote)

Students consider the change in internal energy during three different processes involving a container of water vapor on a stove. Using the 1st Law of Thermodynamics, students reason about how the internal energy would change and then compare this prediction with data from NIST presented as a contour plot.*assignment*Spin Fermi Estimate*assignment*Homework##### Spin Fermi Estimate

Quantum Fundamentals 2023 (2 years) The following two problems ask you to make Fermi estimates. In a good Fermi estimate, you start from basic scientific facts you already know or quantities that you can reasonably estimate based on your life experiences and then reason your way to estimate a quantity that you would not be able guess. You may look up useful conversion factors or constants. Use words, pictures, and equations to explain your reasoning:- Imagine that you send a pea-sized bead of silver through a Stern-Gerlach device oriented to measure the z-component of intrinsic spin. Estimate the total z-component of the intrinsic spin of the ball you would measure in the HIGHLY improbable case that every atom is spin up.
- Protons, neutrons, and electrons are all spin-1/2 particles. Give a (very crude) order of magnitude estimate of the number of these particles in your body.

- Thermal and Statistical Physics 2020 The pressure of water vapor over ice is 518 Pa at \(-2^\circ\text{C}\). The vapor pressure of water at its triple point is 611 Pa, at 0.01\(^\circ\text{C}\) (see Estimate in \(\text{J mol}^{-1}\) the heat of vaporization of ice just under freezing. How does this compare with the heat of vaporization of water?