*group*Ice Calorimetry Lab*group*Small Group Activity60 min.

##### Ice Calorimetry Lab

The students will set up a Styrofoam cup with heating element and a thermometer in it. They will measure the temperature as a function of time, and thus the energy transferred from the power supply, from which they compute changes in entropy.*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*Energy and heat and entropy*face*Lecture30 min.

##### Energy and heat and entropy

Energy and Entropy 2021 (2 years)latent heat heat capacity internal energy entropy

This short lecture introduces the ideas required for Ice Calorimetry Lab or Microwave oven Ice Calorimetry Lab.*group*Name the experiment (changing entropy)*group*Small Group Activity30 min.

##### Name the experiment (changing entropy)

Energy and Entropy 2021 (2 years) Students are placed into small groups and asked to create an experimental setup they can use to measure the partial derivative they are given, in which entropy changes.*group*Name the experiment*group*Small Group Activity30 min.

##### Name the experiment

Energy and Entropy 2021 (3 years) Student groups design an experiment that measures an assigned partial derivative. In a compare-and-contrast wrap-up, groups report on how they would measure their derivatives.*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.*assignment*Heat of vaporization of ice*assignment*Homework##### Heat of vaporization of ice

Vaporization Heat 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?*group*Using $pV$ and $TS$ Plots*group*Small Group Activity30 min.

##### Using \(pV\) and \(TS\) Plots

Energy and Entropy 2021 (2 years) Students work out heat and work for rectangular paths on \(pV\) and \(TS\) plots. This gives with computing heat and work, applying the First Law, and recognizing that internal energy is a state function, which cannot change after a cyclic process.*assignment*Heat capacity of vacuum*assignment*Homework##### Heat capacity of vacuum

Heat capacity entropy Thermal and Statistical Physics 2020- Solve for the heat capacity of a vacuum, given the above, and assuming that photons represent all the energy present in vacuum.
- Compare the heat capacity of vacuum at room temperature with the heat capacity of an equal volume of water.

*group*Heat and Temperature of Water Vapor (Remote)*group*Small Group Activity5 min.

##### Heat and Temperature of Water Vapor (Remote)

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.-
This question is about the lab we did in class: Ice Calorimetry Lab.
**Plot your data I**Plot the temperature versus total energy added to the system (which you can call \(Q\)). To do this, you will need to integrate the power. Discuss this curve and any interesting features you notice on it.**Plot your data II**Plot the heat capacity versus temperature. This will be a bit trickier. You can find the heat capacity from the previous plot by looking at the slope. \begin{align} C_p &= \left(\frac{\partial Q}{\partial T}\right)_p \end{align} This is what is called the*heat capacity*, which is the amount of energy needed to change the temperature by a given amount. The \(p\) subscript means that your measurement was made at constant pressure. This heat capacity is actually the total heat capacity of everything you put in the calorimeter, which includes the resistor and thermometer.-
**Specific heat**From your plot of \(C_p(T)\), work out the heat capacity per unit mass of water. You may assume the effect of the resistor and thermometer are negligible. How does your answer compare with the prediction of the Dulong-Petit law? -
**Latent heat of fusion**What did the temperature do while the ice was melting? How much energy was required to melt the ice in your calorimeter? How much energy was required per unit mass? per molecule? **Entropy of fusion**The change in*entropy*is easy to measure for a reversible isothermal process (such as the slow melting of ice), it is just \begin{align} \Delta S &= \frac{Q}{T} \end{align} where \(Q\) is the energy thermally added to the system and \(T\) is the temperature in Kelvin. What is was change in the entropy of the ice you melted? What was the change in entropy*per molecule*? What was the change in entropy per molecule divided by Boltzmann's constant?-
**Entropy for a temperature change**Choose two temperatures that your water reached (after the ice melted), and find the change in the entropy of your water. This change is given by \begin{align} \Delta S &= \int \frac{{\mathit{\unicode{273}}} Q}{T} \\ &= \int_{t_i}^{t_f} \frac{P(t)}{T(t)}dt \end{align} where \(P(t)\) is the heater power as a function of time and \(T(t)\) is the temperature, also as a function of time.