## Activity: Microwave oven Ice Calorimetry Lab

Energy and Entropy 2021 (2 years)
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.
What students learn This lab gives students a chance to take data on the first day of class (or later, but I prefer to do it the first day of class). It provides an immediate context for thermodynamics, and also gives them a chance to experimentally measure a change in entropy. Students are required to measure the energy required to melt ice and raise the temperature of water, and measure the change in entropy by integrating the heat capacity.

In this lab, we will be measuring how much energy it takes to melt ice and heat water. I have modified this lab to work with a microwave oven that you're likely to have at home.

##### Before the lab

Before the day of the lab, you will need to collect your equipment. If you do not have a microwave oven, or do not have a liquid measuring cup, you will need to use the data from another student in your group. If you do have a microwave and a way to measure the volume or mass of water, please be ready to do this lab during class.

You will need the materials below. Ideally the day before the lab you will put about 500 mL (or even more) of water into a container (not a glass jar, which could break) and put it into the freezer so you will have a large chunk of ice. This will make it easier to separate the ice from the melt water when you melt it. If you do not do this you can still use ice from an ice cube tray, but then it will really help to also have a collander or seive to help separate ice from water.

##### Materials:
• Microwave-safe bowl or mug
• Microwave oven
• Kitchen scale or liquid measuring cup
• Ice and water
• Thermometer (if available)

This is the home version of Ice Calorimetry Lab for when there is a pandemic, or if you want students to do the activity at home. The accuracy students can get with a microwave oven is surprising, so I may adapt this to be a "home lab" even when we are teaching in person.

While the measurements are being taken, I asked the students a couple of small-whiteboard-questions, “What is heat?” and “What is entropy?”. I then lecture on what the heat capacity $C_p$ is, and how they could extract it from their data, and on how they can calculate entropy from their measurements: $\Delta S = \int \frac{dQ}{T}$.

We will be using a microwave oven to measure how much energy it takes to melt ice and how much energy it takes to boil water. If you have a thermometer, you can also measure how much energy it takes to raise its temperature. Our experimental unit of energy will be “seconds in the microwave.” It's not a great unit of measure. A microwave may not always output equal power independent of what is in it, so we'll try not to change too much the amount of ice or water in the oven.

In the analysis, you can use the nominal power of the microwave (as written somewhere on the inside or outside of your oven) to approximately convert this to Joules, but keep in mind that this conversion is dubious on many fronts. There will be energy wasted in the electronics of the microwave, which is not transmitted to the ice. Also the documented power is probably rounded up, because it is used by electricians to determine whether the device is safe to put on a circuit, and for that purpose it is acceptable to use less than the documented power, but not more. We could do better by measuring the current drawn (and the line voltage), but I doubt you have that equipment in your kitchen.

##### Melting ice
We will start by measuring how much energy it takes to melt a gram of ice. You will want maybe 500 mL of ice, or perhaps two ice cube trays. Prepare your ice for this experiment by putting it in a bowl of water for a bit. This will raise its temperature to zero Celsius. Put a bunch of ice (500 mL or two ice cube trays) into a microwave-safe bowl.
1. Microwave the ice for a minute.
2. Pour out the liquid water (possibly through a seive or a collander) into a liquid measuring cup to see how much of the ice was melted. Alternatively you could measure the mass of the melt water with a scale.
3. Repeat, but increase the time significantly if you didn't melt an eaasily measurable amount of water. Stop when you've melted at least half of your ice.

##### Boiling water
We will now measure how much energy it takes to boil water. If you have a glass measuring cup, fill it to the highest mark with water. Add a pebble to the measuring cup (or bowl). Then microwave it until it reaches a full rolling boil. At this point the water should be 100° Celsius.
1. Put the water in the microwave, and heat it for three minutes.
2. Measure the amount of water remaining either by volume or mass.
3. Repeat, but increase the time significantly if you didn't boil an eaasily measurable amount of water. Stop when you've boiled away at least half of your water.

##### Heating water (optional)
Now if you have a thermometer, you can find out how much energy it takes to raise the temperature of water. Start by filling a cup with water, making sure to measure its mass or volume.
1. Measure the temperature of the water and write it down.
2. Put the cup in the microwave for a little while (start with 30 seconds or a minute probably), and write down how long you heated it.
3. Repeat until it reaches boiling. Increase the time interval if your water does not change temperature by an easily measurable amount.

• face Energy and heat and entropy

face Lecture

30 min.

##### Energy and heat and entropy
Energy and Entropy 2021 (2 years)

This short lecture introduces the ideas required for Ice Calorimetry Lab or Microwave oven Ice Calorimetry Lab.
• group Ice Calorimetry Lab

group Small Group Activity

60 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.
• assignment Ice calorimetry lab questions

assignment Homework

##### Ice calorimetry lab questions
This question is about the lab we did in class: Ice Calorimetry Lab.
1. 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.
2. 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.
3. 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?
4. 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?
5. 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?
6. 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.
• 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 Name the experiment (changing entropy)

group Small Group Activity

30 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.
• face Phase transformations

face Lecture

120 min.

##### Phase transformations
Thermal and Statistical Physics 2020

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 Name the experiment

group Small Group Activity

30 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.
• assignment Hockey

assignment Homework

##### Hockey
Central Forces 2022 (2 years)

Consider the frictionless motion of a hockey puck of mass $m$ on a perfectly circular bowl-shaped ice rink with radius $a$. The central region of the bowl ($r < 0.8a$) is perfectly flat and the sides of the ice bowl smoothly rise to a height $h$ at $r = a$.

1. Draw a sketch of the potential energy for this system. Set the zero of potential energy at the top of the sides of the bowl.
2. Situation 1: the puck is initially moving radially outward from the exact center of the rink. What minimum velocity does the puck need to escape the rink?
3. Situation 2: a stationary puck, at a distance $\frac{a}{2}$ from the center of the rink, is hit in such a way that it's initial velocity $\vec v_0$ is perpendicular to its position vector as measured from the center of the rink. What is the total energy of the puck immediately after it is struck?
4. In situation 2, what is the angular momentum of the puck immediately after it is struck?
5. Draw a sketch of the effective potential for situation 2.
6. In situation 2, for what minimum value of $\vec v_0$ does the puck just escape the rink?

• assignment Icecream Mass

assignment Homework

##### Icecream Mass
Static Fields 2022 (4 years)

Use integration to find the total mass of the icecream in a packed cone (both the cone and the hemisphere of icecream on top).

• group Using $pV$ and $TS$ Plots

group Small Group Activity

30 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.

Learning Outcomes