Confirm Gas Laws- Steven Haramis

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Confirm Gas Laws Steven Haramis Student of Ocean County Kinetic Theory of Gases Physics 282 May 29, 2023

Introduction: The comprehension of gas behavior and characteristics necessitates the measurement and analysis of the relationship among pressure, volume, temperature, and the number of gas particles. This report explores experimental data that verifies the principles of Boyle's law, Charles's law, and Gay-Lussac's gas law. Through manipulation of these variables within a virtual environment and examination of the data collected, we can affirm the validity of the three laws. Previous experiments have also been conducted to validate these fundamental laws. A well-known experiment focused on exploring the connection between volume and temperature, which would end up supporting Charles Law. In this experiment, the volume of a sample was graphed against temperature, the resulting graph formed a straight linear line. This observation supported Charles's Law. Another famous past experiment aimed to establish Boyle's Law using a J-shaped tube partially filled with mercury and a gas sealed at one end. By adding additional mercury to increase the pressure of the system, the relationship between volume and pressure were plotted, which in the end confirmed Boyle's Law. Another experiment involved a jar and a piston pressing inside of the jar, where cooling the gas caused a decrease in volume, and heating the system caused an increase in volume. Experiment: Boyle’s, Charles’, and Gay-Lussac’s Laws were tested in the experiment using a virtual air tight chamber. By adjusting the amount of particles in the chamber, length of the chamber and

temperature I was able to test each of the laws. When testing for each law constants changed amongst different laws, but for each law I tested 2 sized particles to get the most accurate results. Also, if a value stayed constant for a law I kept it at the same value for both sizes of particles. For each law I kept many things constant except one, by changing one variable I can prove the laws are true. To ensure that each sample has the same amount of particles I set the width of the box to be 15nm and pumped particles into the box until the pressure was a certain number, for the following samples I followed the same steps to keep the pressure the same. Once the pressure was the same I could adjust the width of the box or temperature. For Boyle’s Law I set three different sized chambers being 5nm, 7.5nm and 15nm long, each chamber had the same amount of particles inside. I recorded the volume of the chamber and the different pressures. For Charles’ law I wanted to test when the lid would come off the chamber, if temperature increases pressure then with enough pressure the lid could pop off of the chamber. I had 3 different volumes being 5nm, 7.5nm and 15nm then I increased the temperature of the chamber and recorded when the lid came off. Lastly for Gay-Lussac’s I had 3 chambers with the same volume (15nm), each chamber had a different temperature (100K, 300K, 500K) and I recorded the pressure inside of each chamber. Heavy Particles (Blue) Sample 1 Sample 2 Sample 3 Volume (width of chamber) 5nm 7.5nm 15nm Pressure 84.2 56.6 atm 28.2 atm

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K Value 300 K 300 K 300 K Table 1: I tested Boyle's Law with the heavy particles, the amount of particles and temperature stayed constant while I changed the volume of the box. Light Particles (Red) Sample 1 Sample 2 Sample 3 Volume (Width of chamber) 5nm 7.5nm 15nm Pressure 117.6 atnm 78.4 atm 39.4 atm Kelvin 300 K 300 K 300 K Table 2: I tested Boyle's Law with the lighter particles, the amount of particles and temperature stayed constant while I changed the volume of the box. Boyle’s Law Results/Discussion: This proves that pressure and volume are inversely proportional, as pressure increases volume decreases and vice-versa. Also, other outside forces do not affect Boyle’s law, for example like temperature, for the both experiments the chamber was 300 K. Pressure increases since there is an increase in the elastic collisions between particles and between the particles and chamber walls, so when volume decreases there is less room for each particle and therefore more collisions. This experiment shows that using different particles does not affect Boyle's law, large or small particles will always follow PV=K.

Heavy Particle (Blue) Sample 1 Sample 2 Sample 3 Volume (Width of Chamber) 5nm 7.5nm 15nm Temperature (when lid pops off) 975 K 1650 K 3100 K Table 3: I tested Charle’s Law with heavy particles: The idea behind the law is that when objects get hotter they expand and the lid will be removed from the chamber. Light Particles (Red) Sample 1 Sample 2 Sample 3 Volume (Width of Chamber) 5nm 7.5nm 15nm Temperature (when lid pops off) 1000 K 1550 K 3050 K Table 4: I tested Charle’s Law with light particles: The idea behind the law is that when objects get hotter they expand and the lid will be removed from the chamber. Charles’ Law Results/Discussion: All of the different sized volumes have the same amount of particles in the chamber, as seen above at larger volumes there has to be a hotter temperature for the lid to pop off of the box. Therefore, it takes longer for objects with a higher volume to heat up and expand. The volume to temperature ratio is close to proportional, from 5 nm to 7.5nm there is about a 1.5 times increase in temperature and volume. From 7.5nm to 15nm there is about a 2 times increase in volume and temperature.The temperature could be off by a couple degrees, since the lid came off at such a high speed I had to take an educated approximation as to what the temperature was.

Heavy Particle (Blue) Sample 1 Sample 2 Sample 3 Temperature 100 K 300 K 500 K Pressure 5.9 atm 16.6 atm 28.4 atm Volume (Width of Chamber) 15nm 15nm 15nm Table 5: I tested Gay-Lussac’s Law with heavy particles. I kept volume constant to ensure the most accurate results. As temperature increases pressure increases and as temperature decreases pressure decreases. Heavy Particle (Blue) Sample 1 Sample 2 Sample 3 Temperature 100 K 300 K 500 K Pressure 6.8 atm 19.2 atm 32.4 atm Volume (Width of Chamber) 15nm 15nm 15nm Table 6: I tested Gay-Lussac’s Law with light particles. I kept volume constant to ensure the most accurate results. As temperature increases pressure increases and as temperature decreases pressure decreases. Gay-Lussac’s Law Results/Discussion: When the temperature of the chamber increases the particles (either small or large) begin to move more rapidly creating more collisions between each other and the walls of the chamber. These collisions increase the pressure inside of the chamber, the opposite happens when the temperature is lower. At around 100K the particles move a lot slower creating less collisions and therefore there is a decrease in pressure. The volume I had to keep constant to receive the most accurate results but volume does not affect this law, a large volume may take longer to heat up but the pressure will still increase (just may take more time).

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Conclusions/Summary: The first set of experiments were designed to prove Boyle’s Law and the relationship between pressure and volume. His law is PV=K which means that pressure and volume are inversely related to each other which is proven in our experiment above. In table 1 and 2 wwe can notice that as the pressure in the chamber increases the volume tends to be lower, and when the pressure in the chamber is smaller the volume of the chamber tends to be larger. In a larger chamber there is more surface area and therefore a smaller chance in which particles collide with each other resulting in a lower pressure. The next set of experiments were completed to prove Charles’ Law (V/T=K), in the experiment the volume of the chamber differed and the lid of the chamber would come off when the pressure became too high due to the addition of heat. The larger the volume the more heat had to be applied to force the lid off of the chamber. The smaller chamber needed less heat since there is a smaller surface area to heat up and there will be more particle collisions (increasing the pressure) and therefore forcing the lid off. Lastly, to prove Gay-Lussac’s the chamber was set to a constant volume for all the samples. His law (PT=K) states that as temperature increases pressure also increases and visa-versa. This is true since pressure is equivalent to the force divided by total volume, when the temperature increases there is more kinetic energy meaning the particles are moving faster. In conclusion the gas laws are confirmed through experimental testing. References: NaderMakarious ,www.sas.upenn.edu/~nader/Boyle’s%20law.htm#:~:text=Robert%20Boyl e%20used%20a%20sealed,the%20volume%20of%20the%20gas. Accessed 29 May 2023.

“Charles and Gay-Lussac’s Law.” NASA , www.grc.nasa.gov/www/k-12/VirtualAero/BottleRocket/airplane/glussac.html. Accessed 29 May 2023. “Liquid Nitrogen Balloon: Charles’ Law.” Chemdemos , chemdemos.uoregon.edu/demos/Liquid-Nitrogen-Balloon-Charles-Law#. Accessed 29 May 2023.

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