5BL Pre-Lab 2 - W24v3

Physics 5BL Pre-Lab 2 - Ideal Gas Laws Winter 2024, UCLA Department of Physics & Astronomy Directions: As you read through the pre-lab, follow along and complete the Google Slides pre-lab submission template to submit your responses to questions below on each slide as indicated. Background: Using PV = nRT (the ideal gas equation) When an ideal gas system (with non-interacting particles) is held in a closed, constant-volume container, the total number of particles N = n N A will be held constant, where n is the number of moles of the gas, and N A = 6.02 x 10 23 molecules per mole is Avogadro’s number. Then gas pressure (P) and gas temperature (T) will be directly related to each other, since R is a constant, R = 8.31 Joules/mole. This model of an ideal gas is very specific and only perfectly applicable over a small range of physical situations, mostly when the gas density is very low. However, relationships between the physical parameters hold true in a qualitative sense for a much wider range of situations. For example, air at room temperature is a nearly ideal gas. Preparation for Activity 1 - Estimation of Absolute Zero You will collect data using an apparatus to heat and isolate a constant volume air pocket by heat transfer from electrically heated water. This setup should emulate a closed, ideal gas system, where pressure and temperature should correlate as predicted by the ideal gas law. If the system behaves like an ideal gas at constant volume, then changing the temperature of the system should have a predictable effect on the pressure of the system. There should be a linear relationship that follows the ideal gas equation PV=nRT, or P = (nR/V) * T. If the ideal gas relation holds in this physical system, you can use the gas pressure measurements with rising temperature to answer an important question about what happens to a gas as P → 0: what is this corresponding temperature point called Absolute Zero (zero Kelvin; 0 K), and what is its value on the Celsius Scale ( ℃ )? For many years, scientists defined temperature with only a relative scale, either the Celsius or Fahrenheit metric, where “zero” temperature corresponded to something that was cold, relative to those temperatures experienced in everyday life, but that still had thermal energy in the system. We know that 0 ℃ or 0 ℉ is not the coldest an object can be, because one can find weather reports of air temperatures < 0 ℃ or < 0 ℉ . If it is possible to make something colder, then it cannot be at absolute zero, because heat is able to transfer from it, and it clearly is not at “zero thermal energy.” In order to assess an absolute scale for temperature, you must determine the temperature where there is zero thermal energy. This is possible by recasting the question as: what is the temperature where since there is no thermal energy, there is no pressure that the gas is exerting on the walls of the system? In this portion of your experiments, you will be able to use your temperature and pressure measurements to extrapolate the temperature in Celsius measurements whereby a system has no thermal energy and exists at Absolute Zero. This is quite a phenomenal physics application, given that you do not have any cooling equipment and that in your experiment you are actually increasing your air temperature to see how pressure depends on temperature in an ideal gas. See Figure 1 for the “ingredients” that you will use to construct your Activity 1 experiments. In thermodynamics terms, the system is the air inside the metal cylinder, and the surroundings is the hot water kettle (filled with water), so think about how you will connect the tubing and the pressure sensor to the air-filled metal container to create a closed environment. Practically, you must strap the temperature sensor to the metal air-filled container with rubber bands. Consider how to avoid contact of the metal cylinder with the metal heating element. How can you

Physics 5BL Pre-Lab 2 - Ideal Gas Laws Winter 2024, UCLA Department of Physics & Astronomy avoid/minimize the transfer of thermal energy in a non-uniform way that would heat up the air in the cylinder at a different rate than the metal container? In other words, how important is it for your experiment for the gas and its container to remain in thermal equilibrium? Figure 1: inventory of equipment for Activity 1. You are responsible for assembling this equipment yourself, such that you can simultaneously measure the pressure and temperature of the system by heating surroundings and having a thermal energy transfer between the surroundings into the system. Here, the system is the air inside the metal cylinder, and the surroundings is the hot water kettle (filled with water). Preparation for Activity 2 - Applications to Blood Pressure You will explore how pressure and volume are related in the context of human blood pressure, inside of the human arm. Our own human blood pressure and heart rate is explored. While the model of an ideal gas may not be the best model to apply to our fluid-filled vasculature, the pressure and volume relationship in an ideal gas model has a conceptual parallel to how our heart creates blood pressure that can help make sense of medical blood pressure readings. Figure 2: human wrist blood pressure sensor for Activity 2. Use this sensor first to determine your own blood pressure and heart rate. To use, strap the sensor tightly to your wrist, and hold your wrist still at the same level as your heart. Failure to stay still or hold your wrist at your heart will give inaccurate readings. (You will determine the reason for this next week.)