Lab9AtmosphericRetentionCompletedCBuckland

Carissa Buckland

Atmospheric Retention 9-5 PRE-LAB QUESTIONS These questions must be answered before you show up to your lab class. You will not be able to start the lab exercise without the answers to these questions. A quiz based on these questions will be given at the beginning of the lab session. 1. What is escape velocity? Escape velocity is the lowest velocity a body must have in order to escape the gravitational attraction of a planet, moon, star, or other celestial body. 2. What is the escape velocity of Earth? 11.2 kilometers per second 3. How is escape velocity related to the mass of a planet? to the radius of a planet? Escape velocity depends on the mass and radius of a planet. V escape = √ 2𝐺𝐺𝐺𝐺 𝑅𝑅 where G is Newton’s Gravitational Constant of 6.67x10 -11 Nm 2 /kg 2 , M is planetary mass, and R is planetary radius. 4. What does the temperature of a gas represent? The average kinetic energy of the particles in a gas is represented by the temperature. 5. Do all particles in a gas move at the same speed? If not, what does the distribution of speeds look like for a given temperature? Not every molecule in a given gas moves at the same speed/temperature. Each gas molecule has a slightly different kinetic energy. Because gases have the same kinetic energy at the same temperature, lighter molecules will move faster, and heavier molecules will move more slowly. 6. What is the difference between the average speed, the most probable speed and the rms speed of a gas particle? Average speed is the average of all the magnitues of the individual moving gas molecules. Most probable speed is the speed that is being attained by the greatest amount of moving gas molecules. Rms speed is the square root of all the mean squared speed of all moving gas particles. V rms = √ 3𝑘𝑘𝑘𝑘 𝑚𝑚 where T is temperature, m is mass of gas, and k is kinetic energy. 7. How do their values compare? Probable speed is greater than average speed which is great than rms speed. V p > V avg > V rms 8. What fraction of particles will have a speed less than the average speed? More than half of the particles 9. How does the speed distribution of gas particles vary with temperature? If the temperature increases, the speed distribution increases. If temperature decreases, the speed distribution decreases.

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Atmospheric Retention 9-10 1 500 1500 H 2 is very quickly lost since it only has a mass of 2u and its most probable velocity is greater than the escape velocity, NH 3 is slowly lost since it is a medium mass gas (18u) and a significant fraction of its velocity distribution is greater than 1500 mis, CO 2 is unaffected since its most probable Hydrogen is lost very quickly due to its low mass, the ammonia is lost at a rate that is about half as quick as the hydrogen because of its medium mass, and the carbon dioxide is lost at a much slower rate. Both hydrogen and ammonia are completely lost before the carbon dioxide is even half-way depleted. Reducing the escape velocity allows for all three gases to escape the chamber at a relatively simultaneous rate. Carbon dioxide is moderately slower than ammonia and hydrogen, but is lost nonetheless. Only hydrogen is lost from the chamber, leaving both the ammonia and carbon dioxide present. Neither ammonia nor carbon dioxide are able to escape due to their most probable velocities being lower than 1500 m/s. Again, only hydrogen is lost from the chamber, leaving both the ammonia and carbon dioxide. Neither remaining gas can escape due to their most probable velocities being lower than 1000 m/s. Hyrdogen is rapidily lost, ammonia is slowly depleted, leaving carbon dioxide to slowly exit the chamber. Higher temperatures combined with lowered escape velocities resulted in a greater loss of gases at a higher rate. Lower temperatures and lowered escape velocities resulted in the standard loss of the low mass hydrogen gas, but much slower losses of the larger mass molecules. Gas is most likely to escape the chamber when temperatures are high and escape velocities are low. I Run I T (K) l V esc

Atmospheric Retention 9-11 GAS RETENTION PLOT This simulator presents an interactive plot summarizing the interplay between escape velocities of large bodies in our solar system and the Maxwell distribution for common gases. The plot has velocity on the y-axis and temperature on the x-axis. Two types of plotting are possible: • A point on the graph represents a large body with that particular escape velocity and outer atmosphere temperature. An active (red) point can be dragged or controlled with sliders. Realize that the escape velocity of a body depends on both the density (or mass) and the radius of an object. • A line on the graph represents 10 times the average velocity (10 v avg ) for a particular gas and its variation with temperature. This region is shaded with a unique color for each gas. o If a body has an escape velocity v esc over 10 v avg of a gas, it will certainly retain that gas over time intervals on the order of the age of our solar system. o If v esc is roughly 5 to 9 times v avg , the gas will be partially retained and the color fades into white over this parameter range. o If v esc < 5 v avg , the gas will escape into space quickly. Begin experimenting with all boxes unchecked in both the gases and plot options. 7. Plot the retention curves for the gases hydrogen, helium, ammonia, nitrogen, carbon dioxide, and xenon. Explain the appearance of these curves on the retention plot. The retention plots are very similar in appearance, with the speed (km/s) of the gases rising with an increase in temperature (K). Hydrogen has the lowest retention curve, meaning it escapes quickly from an atmosphere. Nitrogen and ammonia have very similar curves. Carbon dioxide has a higher retention curve than the three aforementioned gases. Xenon has the highest retention curve and also the highest mass of the gases. Check show gas giants in the plot options panel. 8. Discuss the capability of our solar system's gas giants to retain particular gases among those shown. Gas giants are able to retain particular gases because of the high escape velocities that these planets have, and their speeds are greater than 10 x v avg .

Atmospheric Retention 9-13 POST-LAB QUESTIONS 1. Earth and the Moon are located roughly the same distance away from the Sun, yet Earth has a permanent atmosphere while the Moon does not. Explain why. The gravity of Earth is greater than that of the Moon. The Moon’s low surface gravity is unable to retain its atmosphere. 2. Mercury and Mars have similar surface gravities, yet Mars has a permanent atmosphere while Mercury does not. Explain why. Mercury’s thin atmosphere is constantly blown away by the extreme temperature of the Sun and solar winds. 3. Earth's primary atmosphere consisted of hydrogen and helium, yet today it is now mostly nitrogen with some oxygen. Why did Earth's atmospheric composition change over time? Planetary surface changes, temperature changes, and the introduction of photosynthetic plant life changed Earth’s atmospheric composition. 4. Both Venus and Mars have atmospheres that are predominantly carbon dioxide while Earth only has trace amounts, even though it is gravitationally strong enough to hold on to it. How do we account for this difference? Earth’s large bodies of liquid water account for the difference in carbon dioxide concentrations.