The Fire Syringe, State Variables and Ideal Gas Law

The Fire Syringe

In this experiment, we have an air-tight cylinder with a piston that allows for a variation in volume. We want to know the temperature of the gas (air) inside the cylinder after it is compressed quickly. We derive an equation for the final temperature as shown in the picture below.

We made all of the necessary measurements and calculations to find the initial temperature volume. We used a thermometer inside the cylinder to measure the temperature of the air. Next we used a caliper to measure the diameter (from which we derived the radius) and the length of the chamber before compression. The volume was calculated using V=(pi)(L)(R)^2. We placed a small piece of cotton at the bottom of the chamber and quickly decreased the volume by pushing on the chamber. The video below shows this action at in slow motion.

The cotton inside ignited instantly and left a small black ring around the inside surface of the cylinder. This marked the final length (L) needed in calculating the final volume. We used the same caliper to measure this length and calculated our final volume. With this information, we were then able to calculate the final temperature of the gas inside the cylinder at the final volume.

Our calculated final temperature came out to be 792.5 K which is 967.1 *F. Compared to Ray Bradbury's novel Fahrenheit 451 (where the title refers to the temperature that paper will ignite), we are not surprised that the cotton mass caught fire. 

Since the volumes were calculated values, I needed to propagate for the uncertainties of initial and final volumes, respectively. I found the initial volume to have an uncertainty of 182 mm^3 and the final volume to have an uncertainty of 42.1 mm^3. These values were used in the next step, when propagating for the uncertainty in temperature.

Using the uncertainty for initial temperature to be half a degree Celsius or half a Kelvin, and using the uncertainties for volume from the previous step, I was able to propagate for uncertainty in the final temperature. The uncertainty cam out to be 113 K. So our final experimental temperature is 793 K +/- 113K.

ActivPhysics: State Variables and Ideal Gas Law

The picture above shows the answers and solutions for the ActivPhysics assignment we conducted in class. The assignment consisted of interactive simulations on the ActivPhysics website. We learned about the relationships between the state variables in the ideal gas law. The problems consisted of situations where certain variables were kept constant and we needed to solve for a pressure of volume.