Charles's Law: How Temperature changes gas Volume

While working on the greenhouse experiment, I put a balloon with carbon dioxide inside the freezer to lower the density to ensure it would stay at the bottom of the jar while doing the experiment. One thing I noticed is that the balloon shrunk. I found this interesting and I decided to investigate more.

To understand what happened we need to realize that a gas consists of molecules that are moving in space. The hotter the gas is the faster they move. Conversely the colder it is the slower they move. In my case the gas with CO2 inside the freezer became cooler and the molecules inside the balloon started to move slower which means they don't push as hard against the balloon, so then the ballon shrinks.

It turns out that there is a law in physics called Charles's Law that explains the relationship between the temperature and the volume of a gas. The law states that the volume of a fixed amount of gas is directly proportional to its absolute temperature, provided the pressure remains constant. Mathematically is expressed: V1/T1 = V2/T2.

The temperature is absolute temperature, meaning in Kelvin.

To take better measurements I decided to do an experiment with my big syringe. As you can see I loaded it with 80ml of air and I sealed the tip with blue tag and some tape. The temperature in the room was 24C. I then put the syringe in the freezer.

After a while I put the thermometer in the freezer, let the reading stabilize and I took both the syringe and the thermometer out. As you can see the syringe had shrunk to 75ml and thermometer measured -9C.

Let's do the math:

    T1 = 22 degrees celsius + 273.13 = 295.13 Kelvin

    T2 = -9 degrees celsius + 273.13 = 264.13 Kelvin

    V2 = V1 x T2 / T1 = 80 x 264.13 / 295.13 = 72ml

As you can see in the previous photo, we measure V2 = 75ml. So it shrunk but not as much as Charles Law predicted. It could be due to the friction of the rubber inside the syringe.

I also to see the opposite effect by heating it up. In theory it should expand. For this part of the experiment I set also the initial volume to 80ml and then I heated up with a hair dryer. As you can see it expanded all the way to 85ml.

I don't have a thermometer inside the syringe but I can use now Charles's law to get an estimation of what temperature it reached during the experiment.

T2 = V2 x T1 /V1 = 84ml x 295.13K / 80ml = 309.88 K = 36.7 degrees Celsius

Again, maybe the friction prevented it from expanding more which would have given us a higher estimated temperature.