Lab_3

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Bergen Community College *

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PHY 222

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Physics

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Apr 3, 2024

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Lab Assignment 3: Charles’ Law and Entropy Instructor’s Overview In this lab, we will turn our attention to two topics related to thermal energy: We will execute an experiment that explores Charles’ Law which states that, if pressure is held constant, the temperature of the gas is directly proportional to the volume of the gas. We will explore a profound consequence of the second law of thermodynamics - the concept of entropy. To accomplish this we will carry out an experiment using dice as our test vehicle. This lab is based on elements of Lab 15 and Lab 18 of your eScience Lab kit. We will be performing the following experiments: Experiment 1 of Lab 15 Experiment 2 of Lab 18 including Prelab questions 2 and 3 Take detailed notes as you perform the experiment and fill out the sections below. This document serves as your lab report. Please include detailed descriptions of your experimental methods and observations. What you’ll need for this lab activity From the eScience kit Styrofoam cup Stopwatch Thermometer 10 ml sealable syringe and graph paper (Found in the Ideal Gas Law baggie). Dice (Found in Second Law of Thermodynamics baggie). JWH 1 Physics II Physics Physics II II
You provide Crushed ice Pencil Water Experiment Tips : Exercise care when working around hot water. In the Charles's law lab, use the tip of the rubber stopper in the syringe for your volume reading: Please execute multiple trials with the cold and hot water baths. Gently push in the stopper of the syringe and let the volume return to equilibrium. Then record the volume in the provided table. Date : 02/1/24 Student : Anthony Putrino Abstract Jacques Charles, in the law of entropy, expresses that for a certain quantity of gas at constant pressure, as the temperature increases, the volume of the gas increases and as the temperature decreases, the volume of the gas decreases. This is because the temperature is directly related to kinetic energy due to the movement of gas molecules. So, for a certain amount of gas at a given pressure, the higher the speed of the molecules (temperature), the greater the volume of the gas. The General Law of the State of Gases is a combination of Boyle's and Charles's laws. This indicates how pressure, volume, and temperature are related to each JWH 2 Physics II
other, when one of these variables is changed, it affects at least one of the other two variables. The second law of thermodynamics states that there is a tendency in nature to move towards a state of greater molecular disorder. Entropy is a measure of disorder, solid crystals, the most structured form of matter, have very low entropy values. The more highly disorganized gases have high entropy values. The potential energy of isolated energy systems that is available to do work decreases with increasing entropy. The second law of thermodynamics states that heat can never be transferred, by its own effort, from a zone of lower temperature to another of higher temperature. Macrostates describe the behavior of an entropy system Introduction The following report will talk about the laboratory carried out on the gas laws and the importance of their respective identification. It will be analyzed, its changes and transformations, how temperature, pressure, and volume can affect the system according to the law that governs it. Various experiments indicating their changes will be discussed together with the help of high and low-temperature water containers. In addition, the probability will be studied and how entropy is present in daily life Material and Methods Styrofoam cup Stopwatch Thermometer 10 ml sealable syringe and graph paper (Found in the Ideal Gas Law baggie). Dice (Found in Second Law of Thermodynamics baggie). Crushed ice Pencil Water Lab 15 Experiment 1: Charles’ Law Results/Observations Enter your data in the following table and record your observations: JWH 3 Physics II
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Trial Temperature ( C) Volume (mL) Initial volume Room temperature = 25 5 Hot water trial 1 47 9.3 Hot water trial 2 46 9.1 Hot water trial 3 52 10 Hot water trial 4 49 9.4 Hot water trial 5 50 9.8 Cold water trial 1 1 1 Cold water trial 2 1 1 Cold water trial 3 0 1 Cold water trial 4 1 1 Cold water trial 5 0 1 Lab 15 Experiment 1: Charles’ Law – Analysis and Discussion Based on your experimental results, please answer the following questions: 1. What happened to the volume of gas when the syringe was exposed to various temperature conditions? Using the concepts explored in the Introduction, describe why this occurred, keeping in mind the definition of temperature. The volume of gas when the syringe was exposed to various temperature conditions, had changes. Since if the temperature is reduced its volume is reduced, the average molecular energy in the air is reduced, this allows an easy compression of the syringe. While when the temperature increased, the compression of the syringe was difficult, due to the increase in volume 2. Plot your volume and temperature data in Excel. Temperature (remember to use degrees Celsius) should be on the x-axis and volume (mL) on the y-axis. Perform a linear regression on your volume vs. temperature data in Excel. Refer to the Module 1 instructor commentary on linear regression for guidance. Insert your Excel plot below: JWH 4 Physics II
3. Why can you assume a linear relationship (a straight-lined slope)? A linear relationship can be assumed, since as we have commented the volume and temperature of a gas at constant pressure are directly related 4. Using your linear regression equation set Y (volume) equal to zero and solve for X (temperature). Show your work below: y = 0.1766x + 0.8693 ; y = 0 x = - 4.92 5. At what temperature does your line intersect the x-axis (temperature axis)? x= - 4.92 6. Is your measurement of absolute zero close to the actual value (-273 °C)? Calculate a percent error. How might you change the experiment to get closer to the actual value? T = -4.92°C (Absolute zero) JWH 5 Physics II
% =|(-273+4.92) / (-273)| x 100 % = 98% In order to reduce the large percentage of the error, it is necessary to have more suitable equipment to be able to reach absolute zero. They are needed from syringes, to cooling equipment to be able to obtain a more reasonable error 7. Would it be possible to cool a real gas down to zero volume? Why or why not? What do you think would happen before that volume was reached? It would not be possible, since for very low temperatures, it is very likely that the gas will condense first into a liquid Lab 18 Experiment 2: Probability of States Results/Observations Enter your data in the following tables: Note : k is the Boltzmann constant, 1.38 x 10 -23 J/K. Prelab Question 2 - Microstate Data for 2 Dice Macrostate Possible Microstates (Dice Combinations) Number of Microstates ( ) Entropy S = k ln( ) 2 1 1 0 3 2 2 9.57 x 10 -24 4 3 3 1.52 x 10 -23 5 4 4 1.91 x 10 -23 6 5 5 2.22 x 10 -23 7 6 6 2.47 x 10 -23 8 5 5 2.22 x 10 -23 9 4 4 1.91 x 10 -23 10 3 3 1.52 x 10 -23 JWH 6 Physics II
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11 2 2 9.57 x 10 -24 12 1 1 0 Prelab Question 3 - Macrostate Probability Data Macrostate Probability of Rolling Macrostate 2 1/36 = 0.03 3 2/36 = 0.06 4 3/36 = 0.08 5 4/36 = 0.11 6 5/36 = 0.14 7 6/36 = 0.17 8 5/36 = 0.14 9 4/36 = 0.11 10 3/36 = 0.08 11 2/36 = 0.06 12 1/36 = 0.03 Insert your graph of probability vs. macrostate below. I suggest using the column chart graph type in Excel. Lab 18 Experiment 2 – Dice Macrostate Probability Data – 100 Trials JWH 7 Physics II
Macrostate Number of Occurrences (Tally Marks) Total Occurrences 2 2 2 3 4 4 4 11 11 5 11 11 6 9 9 7 18 18 8 16 16 9 16 16 10 7 7 11 5 5 12 1 1 Lab 18 Experiment 2: Probability of States – Analysis and Discussion Based on your experimental results, please answer the following questions: 1. Create a graph of the number of occurrences of each macrostate. For consistency, I suggest using the column chart graph type in Excel. Insert the graph below. How does this graph compare to the graph you created in Pre- Lab Question 3? JWH 8 Physics II
JWH 9 Physics II
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2. Given your data for one hundred rolls, calculate the probability of rolling one specific macrostate. How does this compare to the percentages you calculated in Pre-Lab Question 3? To answer this question, fill in the following table. Note : Your experimental probability percentage for each macrostate is simply the observed tally since we executed 100 trials. Macrostate Theoretical Probability * Experimental Probability Percent Difference 2 0.03 0.02 33% 3 0.06 0.04 33% 4 0.08 0.11 38% 5 0.11 0.11 0% 6 0.14 0.09 36% 7 0.17 0.18 6% 8 0.14 0.16 16% 9 0.11 0.16 45% 10 0.08 0.07 38% 11 0.06 0.05 17% 12 0.03 0.01 67% * From the table in Prelab question 3. 3. If you repeated this experiment four times, would you expect similar results? Why or why not? He would not expect similar results, because his behavior is very particular 4. How would your results be different if you rolled the dice fifty times? Five hundred times? The more launch opportunities exist, the possibility of an ideal behavior is more distant JWH 10 Physics II
Optional extra credit experiment Procedure 1. Place 24 coins face-up on a large tray. 2. Move the tray up and down rapidly to jostle the coins. 3. Carefully count and record the number that are still face-up. 4. Repeat steps 2-3 for a total of 15 trials. 5. Transfer your data into Excel and plot the results.  Your plot should have “count” for the y-axis and “trial number” on the x-axis.  The plot should show the number of heads and the number of tails for each trial, including the initial state of 24 heads and 0 tails. Insert your plot in the lab report and answer the questions below. Excel plot Question 1 : After starting with an “ordered” set in step 1, how likely do you think it is to arrive back in a state of “order” after shaking the tray numerous times (i.e., end with all heads or all tails)? Ultimately, the number of possibilities is very large and only one of them corresponds to the ordered structure (all faces). The other possibilities, many more, are situations in which there is no order. Question 2 : How does this experiment demonstrate the concept of entropy? The disorder of a system can be expressed quantitatively by means of a quantity called entropy. The Second Principle of Thermodynamics is a statement about JWH 11 Physics II
the type of probabilistic behavior illustrated by this example. The spontaneous change of a system goes from less possibility to greater probability, to achieve it generates greater entropy. The disorder is much more likely than in order. There is a tendency to go from low entropy to high entropy. Conclusions In this experiment I was able to come up with several conclusions, such as when the pressure increases and decreases, a kind of cycle is formed in which energy is not lost at any time and everything returns to its normal state, therefore obeying the first law of thermodynamics where it tells us about conservation of energy. Also, this experiment makes reference to the ideal gas laws in this case it refers specifically to Boyle's law in which it tells us that “the pressure exerted by a physical force is inversely proportional to the volume of a gaseous mass, as long as its temperature remains constant”, and that exactly is fulfilled in the development of the experiment. The experiment gives us a rather curious data and also important to analyze in which a small but no less important variation in temperature is noted due to the sudden decompensation that occurs when the pressure increases and decreases, it returns to room temperature due to the heat flow from the environment into the syringe. JWH 12 Physics II
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