8.1 Hot Air Balloon—Density, Temperature/Volume Part 1

  1. Introduction

    In this session, we will build a hot air balloon from simple, "around the house" materials. This session is the first in a series that will allow us to describe an "ideal gas".

  2. Objectives

    We will build a hot air balloon and use it to show that its lifting ability is some function of the temperature of the air inside the balloon. We will then conjecture on why this should be so. We will then create a mathematical expression that describes the lifting ability as a function of the temperature of the air inside the balloon.

  3. Materials and building instructions.

    There are lots of web sites that describe how to build a small hot air balloon. I suggest that you do not use the tissue paper version because it takes to long too construct. The plastic bag version is much faster although slightly heavier. I have included a picture of a typical plastic bag hot air balloon for some basic guidance in its construction.

    Home made, plastic bag, hot air balloon
  4. Vocabulary
  5. Presentation

    Have the demonstration balloon ready before class. When the students arrive, enlist four of them to help launch the balloon: one to hold the top corners of the balloon, another to light the candles, another to hold the tether line, and the forth to be the safety offices and staff the fire extinguisher.

    When the balloon starts to rise the first time, let it go and just have fun with it. Then bring the focus back to science. "I wonder how much mass this balloon can lift?" Add weight to the balloon. Coins attached to adhesive tape will work nicely. One can also use weights from a balance beam. Try to keep the weight just at the point where the balloon is in equilibrium. That is, it is not rising or falling.

    Light more candles (or use a small propane torch) to get more heat into the balloon. Then, if the balloon starts to rise, add more weight. Be careful because the plastic will start to melt if it gets too hot.

    Then ask the students to invoke the scientific method and see if they can find things to measure, make conjectures/hypotheses, design experiments, and test their hypotheses. My hope is that they will want to build thier own hot air balloon and attempt to measure the amount of mass in equilibrium with the temperature of the air inside the balloon. Be sure to have enough stuff for extra balloons and measuring equipment.

    If there is time or if this session can be spread over two days, change the hot air balloon paradigm to a cold air balloon paradigm. Use liquid nitrogen to fill the balloon with cold "air". (One might be tempted to use dry ice (carbon dioxide) for this demonstration but carbon dioxide is significantly denser than air at the same temperature. Therefore, the results for hot and cold will be inconsistant.) Since air contains a significant fraction of nitrogen, liquid nitrogen will be a very good proxy for air.

    Warning! Both liquid nitrogen and dry ice are extremely cold and can cause severe frostbite within seconds. Be very careful. Do not touch either material nor the containers in which they are stored. Be especially careful about touching the tin can mentioned below.

    Put some liquid nitrogen in a tin can with a long string (at least two feet in length) serving as a handle. Using the string, lower the can into the balloon. Eventually, the cold vapor should fill the now inverted balloon and leak over the top.

    Now ask the students to apply the scientific method and form a hypothesis to describe their observation, devise experiments to test their hypothesis and revise their hypothesis. Hopefully, they will extend their graph from the heating experiment by measuring the weight of the balloon and the temperature of the gas inside the balloon.


    The following section is context information for the instructor.

    We have not learned anything about the concept of density or buoyancy. Those concepts are not really necessary now (with sufficient hand waving) and we will learn about those things later in this course. If we can get the students to understand that the lifting ability of the balloon is a function of temperature, we are successful.

    Recall that the ideal gas law can be written

    PV = KmT

    where P is the pressure, V is the volume, K is some constant that depends on the units we use, m is the mass and T is the temperature. The two things we are measuring are the mass (we will actually use weight but weight is proportional to mass) and the temperature. We will discover in a few lessons that the temperature should be measured in an absolute scale like Kelvins. However, the graph we expect from the students will look like the one just below and it will probably use the Celsius scale. The lifting ability of the balloon will be the weight of the gas in the balloon at room temperature W0 minus the weight of the gas at some higher temperature WT. The ideal gas law tells us that the weight of the gas at a higher temperature will be proportional to 1/T. (P, V, and K are constant.) The graph reflects all that. The negative values of "Lift" mean that the balloon has some weight and as the air gets warmer the apparent weight decreases.

    The temperature range is from about 0°C to 100°C. If the balloon gets much hotter it will be in danger of melting. The lifted weight is just an arbitrary number but the shape of the curve is approximately correct. However, in the range where the balloon is lifting, say 60°C to 100°C the curve will look like a line within experimental error. That is not a problem. Actually, it is a good thing because it will provide an opportunity for the students to modify their hypothesis in a future lesson.

    If there is time to include the liquid nitrogen portion of this session, the graph will clearly show the

    W0-S/T

    form. (Here S is a constant that makes the graph look right.) Then the students will have more data on which to construct a hypotheses.

    Important things for the instructor to remember.

    Today's session does not really demonstrate Charles' law

    V ∝ T

    but it comes close. (The volume remains constant because the excess air leaks out of the balloon. But if it did not leak out, the balloon would grow larger.)

  6. Evaluation

    The first few questions will create and use a definition that we will find helpful.