Linear Expansion and Gas Laws

     This is a picture of the setup for the first experiment that was performed on Wednesday. The setup consists of an aluminum rod with one end connected to a steam generator and the other laid on top of a small pulley. As the steam heated up the rod, the length of the rod would expand and move the pulley through a certain angular displacement. Ultimately, our goal was to find a value for alpha (in the linear expansion equation) of the aluminum rod.

     These are the calculations and relationships used to determine the value for alpha of the aluminum rod. We first had to come up with a relationship between the angular displacement of the pulley and the change in length of the rod. We then used that relationship to solve for delta L and substituted it into a previously solved equation for alpha. That final equation can be seen in the upper right hand corner of the boxed off portion of the whiteboard. We then propagated our uncertainty using only the uncertainty of the length of the rod, which was given to us. Unfortunately, the true value of 2.4*10^-5 lied outside of our calculated range of uncertainty. If we had used more values of uncertainty in our propagation, I believe the true value would have fell into our calculated range.

     The above picture simply shows the two graphs that were constructed using LoggerPro during this experiment. The graph toward the top of the picture shows the relationship of Temperature vs. Time, and the graph on the bottom shows the relationship of Angular Displacement vs. Time.

     The second experiment we conducted on Wednesday was performed in order to calculate the Heat of Vaporization of water. Unfortunately, I was so excited about starting the experiment that I forgot to take a picture of the setup. However, a picture of a similar setup consisting of a Styrofoam cup, thermistor probe, and an immersion heater can be seen on the previous post. We used the immersion heater to boil water initially at room temperature and the thermistor probe to measure the temperature as it increased. The above graph shows the data collected from the experiment. The graph should look a lot smoother than it does in our picture, but there was a bit of technical difficulty that time would not allow us to correct.



     In order to calculate the Heat of Vaporization for water, we simply needed to know the power that the immersion heater supplied, the time it took for the water to boil, and the mass of water that was actually boiled off during the experiment. The average value of power for the entire class was 290W, which we used along with an uncertainty of plus or minus 10W. We then multiplied that by the time it took for the water to boil, 101.5 seconds, in order to find the actual energy that was transferred. After that we divided the amount of energy by the total amount of liquid water lost to get a value of about 1.1*10^6. Finally, we propagated the uncertainty for our calculation. 



 

 

     After the experiment, the values calculated at each table were put into a spreadsheet and the average value was taken. Since the uncertainty we propagated was actually rather small (about 3.9*10^4), we figured that standard deviation would give us a greater value of uncertainty that would hopefully allow the true value of Heat of Vaporization to lie within our calculated range. The process of standard deviation produced a value of uncertainty of 8.58*10^5. However, even taking this massive value of uncertainty into consideration, our percent error was slightly more than 12%. Without the uncertainty, our percent error was 50% given that the true value is 2.256*10^6.

     At the top of the whiteboard are our predictions of what a graph of Pressure vs. Volume and Pressure vs. Temperature would look like. We predicted that pressure would be inversely related to volume and directly related to temperature.

     This is a graph of Pressure vs. Volume that was produced with LoggerPro from a demonstration performed by Professor Mason. As you can see from the graph, our prediction was correct and pressure is indeed inversely proportional to volume. As the pressure in the demonstration was increased, the volume decreased accordingly. The relationship should be P=1/V, but according the LoggerPro it was P=3288/V. I was never able to figure out why this was.



     This is a graph of Pressure vs. Temperature that was produced from another one of Professor Mason's demonstrations. Again, our predictions were correct and the pressure of a gas is directly related to its temperature. As the temperature increases, so does its pressure and vice versa. The relationship is clearly linear as can be seen from the graph.