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.
biotech Experiment
60 min.
assignment Homework
face Lecture
30 min.
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 Small Group Activity
30 min.
group Small Group Activity
30 min.
assignment Homework
Use integration to find the total mass of the icecream in a packed cone (both the cone and the hemisphere of icecream on top).
assignment Homework
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 \(r = a\).
group Small Group Activity
30 min.
assignment Homework
In economics, the term utility is roughly related to overall happiness. Many things affect your happiness, including the amount of money you have and the amount of coffee you drink. We cannot directly measure your happiness, but we can measure how much money you are willing to give up in order to obtain coffee or bagels. If we assume you choose wisely, we can thus determine that your happiness increases when you decrease your amount of money by that amount in exchange for increasing your coffee consumption. Thus money is a (poor) measure of happiness or utility.
Money is also a nice quantity because it is conserved---just like energy! You may gain or lose money, but you always do so by a transaction. (There are some exceptions to the conservation of money, but they involve either the Fed, counterfeiters, or destruction of cash money, and we will ignore those issues.)
In this problem, we will assume that you have bought all the coffee and bagels you want (and no more), so that your happiness has been maximized. Thus you are in equilibrium with the coffee shop. We will assume further that you remain in equilibrium with the coffee shop at all times, and that you can sell coffee and bagels back to the coffee shop at cost.^{*}
Thus your savings \(S\) can be considered to be a function of your bagels \(B\) and coffee \(C\). In this problem we will also discuss the prices \(P_B\) and \(P_C\), which you may not assume are independent of \(B\) and \(C\). It may help to imagine that you could possibly buy out the local supply of coffee, and have to import it at higher costs.
The prices of bagels and coffee \(P_B\) and \(P_C\) have derivative relationships between your savings and the quantity of coffee and bagels that you have. What are the units of these prices? What is the mathematical definition of \(P_C\) and \(P_B\)?
Write down the total differential of your savings, in terms of \(B\), \(C\), \(P_B\) and \(P_C\).
assignment Homework
It has been proposed to use the thermal gradient of the ocean to drive a heat engine. Suppose that at a certain location the water temperature is \(22^\circ\)C at the ocean surface and \(4^{o}\)C at the ocean floor.
What is the maximum possible efficiency of an engine operating between these two temperatures?
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.
Introduction
This lab is very simple to run, but to get it done in one period you'll need to get students working quickly to measure the ice and water and get their heating started. Once their labs are going, there is time to give a middle-of-lab lecture introducing thermodynamics and thermal measurements.
There are two things to keep in mind for this lab. One is that the ice-water cups need to be vigorously stirred, otherwise the hot water (around 4 degrees Celsius) will settle at the bottom while the cold ice floats on the top. The other is that the ice should be cubes (not crushed) and the water should be ice-cold before it is massed out, otherwise too much ice will melt immediately on being added to the water.
Once the measurements are 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: \(\Delta S = \int \frac{dQ}{T}\).
Student Conversations
Many students have difficulties simply measuring the water and ice correctly. Perhaps smaller containers for retrieving water would be good (around the same size as necessary). Or perhaps some basic lab procedures need to be gone over at some point in the Paradigms. Once the basic lab setup was accomplished, students seemed able to do the rest of the lab with no difficulty. -Amanda Abbott
Wrap-up
At the end of the lab, students should know how to calculate the entropy from the change in temperature. Students should be given a few days to do the analysis, and the data that they collect should be distributed to each member of the group.
You will put some mass of ice (about 50g) and ice-cold water (about 150g) into your styrofoam cup. Use the scale to record the mass of the ice and water as you add them to the cup. Finally, add your ice-cold heating element and thermometer through the lid of the cup.
We will be measuring the temperature of the water and the power dissipated in the heating element (which is just a resistor). Thus we can find out how much energy was added to the water, and how this changes the temperature. In order to keep the temperature measurement reasonable, we will need to periodically stir the cup and heat it moderately slowly.
You will be collecting temperature data using the computer, so before you turn on the heater, you should make sure the computer is taking data. Turn on the heater, and write down the time you do so as well as the current and voltage, from which you can find the power dissipated in the resistor. If the current or voltage changes during the course of the experiment, take note of the new values---and the time.