Lab 13

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Apr 3, 2024

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Name: NAAP – Retention of an Atmosphere 1/7 Atmospheric Retention – Student Guide Background Information Work through the background sections on Escape Velocity, Projectile Simulation, and Speed Distribution. Then complete the following questions related to the background information. Question 1: Imagine that asteroid A that has an escape velocity of 50 m/s. If asteroid B has twice the mass and twice the radius, it would have an escape velocity ______________ the escape velocity of asteroid A. a) 4 times b) Twice c) the same as d) half e) one-fourth Question 2: Complete the table below by using the Projectile Simulator to determine the escape velocities for the following objects. Since the masses and radii are given in terms of the Earth’s, you can easily check your values by using the mathematical formula for escape velocity. Object Mass (Mearth) Radius (Rearth) v esc (km/s) v esc (km/s) calculation (optional) Mercury 0.055 0.38 ± ² ± ² 0.055 11.2 4.3 0.38 km km s s § · ¨ ¸ © ¹ Uranus 15 4.0 Io 0.015 0.30 Vesta 0.00005 0.083 Krypton 100 10 • 4. 3 YI 21.7k ¥ (11.2+7)=21.7*7 0.56 KF F, (11.2*7)=0.56*7 0.275K ¥ FÉ (112+7)=0.2 > sky 35.4*75%(11.2*7)=3%4 ' %

NAAP – Retention of an Atmosphere 2/7 Question 3: Experiment with the Maxwell Distribution Simulator. Then a) draw a sketch of a typical gas curve below, b) label both the x-axis and y-axis appropriately, c) draw in the estimated locations of the most probable velocity v mp and average velocity v avg , and d) shade in the region corresponding to the fastest moving 3% of the gas particles. Maxwell Speed Distribution 1 Most Probable 1 ✓ Velocity & average n velocity A ¥ É ¥ 1 fastest 1 moving i Particle speed / mutant "

NAAP – Retention of an Atmosphere 3/7 Gas Retention Simulator Open the gas retention simulator . Begin by familiarizing yourself with the capabilities of the gas retention simulator through experimentation. x The gas retention simulator provides you with a chamber in which you can place various gases and control the temperature. The dots moving inside this chamber should be thought of as tracers where each represents a large number of gas particles. The walls of the chamber can be configured to be a) impermeable so that they always rebound the gas particles, and b) sufficiently penetrable so that particles that hit the wall with velocity over some threshold can escape. You can also view the distributions of speeds for each gas in relation to the escape velocity in the Distribution Plot panel. x The lower right panel entitled gases allows you to add and remove gases in the experimental chamber. The lower left panel is entitled chamber properties . In its default mode it has allow escape from chamber unchecked and has a temperature of 300 K. Click start simulation to set the particles in motion in the chamber panel. Note that stop simulation must be clicked to change the temperature or the gases in the simulation. x The upper right panel entitled distribution plot allows one to view the Maxwell distribution of the gas as was possible in the background pages. Usage of the show draggable cursor is straightforward and allows one to conveniently read off distribution values such as the most probable velocity. The show distribution info for selected gases requires that a gas be selected in the gas panel. This functionality anticipates a time when more than one gas will be added to the chamber. Exercises x Use the pull-down menu to add hydrogen to the chamber. Question 4: Complete the table using the draggable cursor to measure the most probable velocity for hydrogen at each of the given temperatures. Write a short description of the relationship between T and v mp . T (K) v mp (m/s) 300 200 100 1714 MY 1,252M 'S The universal gas constant is 990mn A- 8.3151kg for hydrogen molecules with a weight of M=2

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