Daily Archives: August 19, 2019

200 posts

18.83 … CP Dark Nebulae and the Interstellar Medium. The dark area in Fig. P18.83 that appears devoid of stars is a dark nebula a cold gas cloud in interstellar space that contains enough material to block out light from the stars behind it. A typical dark nebula is about 20 light-years in diameter and contains about 50 hydrogen atoms per cubic centimeter (monatomic hydrogen not H2) at about 20 K. (A light-year is the distance light travels in vacuum in one year and is equal to 9.46 * 1015 m.) (a) Estimate the mean free path for a hydrogen atom in a dark nebula. The radius of a hydrogen atom is 5.0 * 10-11 m. (b) Estimate the rms speed of a hydrogen atom and the mean free time (the average time between collisions for a given atom). Based on this result do you think that atomic collisions such as those leading to H2 molecule formation are very important in determining the composition of the nebula? (c) Estimate the pressure inside a dark nebula. (d) Compare the rms speed of a hydrogen atom to the escape speed at the surface of the nebula (assumed spherical). If the space around the nebula were a vacuum would such a cloud be stable or would it tend to evaporate? (e) The stability of dark nebulae is explained by the presence of the interstellar medium (ISM) an even thinner gas that permeates space and in which the dark nebulae are embedded. Show that for dark nebulae to be in equilibrium with the ISM the numbers of atoms per volume 1N>V2 and the temperatures 1T2 of dark nebulae and the ISM must be related by 1N>V2nebula 1N>V2ISM = TISM Tnebula (f) In the vicinity of the sun the ISM contains about 1 hydrogen atom per 200 cm3. Estimate the temperature of the ISM in the vicinity of the sun. Compare to the temperature of the sun’s surface about 5800 K. Would a spacecraft coasting through interstellar space burn up? Why or why not?

University Physics with Modern Physics lessons by JJtheTutor. Designed to teach students problem solving skills, test taking skills and how to understand the concepts.

18.81 … DATA The Dew Point and Clouds. The vapor pressure of water (see Exercise 18.44) decreases as the temperature decreases. The table lists the vapor pressure of water at various temperatures: Temperature 1 _C2 Vapor Pressure 1Pa2 10.0 1.23 * 103 12.0 1.40 * 103 14.0 1.60 * 103 16.0 1.81 * 103 18.0 2.06 * 103 20.0 2.34 * 103 22.0 2.65 * 103 24.0 2.99 * 103 26.0 3.36 * 103 28.0 3.78 * 103 30.0 4.25 * 103 If the amount of water vapor in the air is kept constant as the air is cooled the dew point temperature is reached at which the partial pressure and vapor pressure coincide and the vapor is saturated. If the air is cooled further the vapor condenses to liquid until the partial pressure again equals the vapor pressure at that temperature. The temperature in a room is 30.0_C. (a) A meteorologist cools a metal can by gradually adding cold water. When the can’s temperature reaches 16.0_C water droplets form on its outside surface. What is the relative humidity of the 30.0_C air in the room? On a spring day in the midwestern United States the air temperature at the surface is 28.0_C. Puffy cumulus clouds form at an altitude where the air temperature equals the dew point. If the air temperature decreases with altitude at a rate of 0.6 C_>100 m at approximately what height above the ground will clouds form if the relative humidity at the surface is (b) 35%; (c) 80%?

University Physics with Modern Physics lessons by JJtheTutor. Designed to teach students problem solving skills, test taking skills and how to understand the concepts.

18.76 .. (a) Calculate the total rotational kinetic energy of the molecules in 1.00 mol of a diatomic gas at 300 K. (b) Calculate the moment of inertia of an oxygen molecule 1O22 for rotation about either the y- or z-axis shown in Fig. 18.18b. Treat the molecule as two massive points (representing the oxygen atoms) separated by a distance of 1.21 * 10-10 m. The molar mass of oxygen atoms is 16.0 g>mol. (c) Find the rms angular velocity of rotation of an oxygen molecule about either the y- or z-axis shown in Fig. 18.18b. How does your answer compare to the angular velocity of a typical piece of rapidly rotating machinery 110 000 rev>min2? 18.77 .. CALC (a) Explain why in a gas of N molecules the number of molecules having speeds in the finite interval v to v + _v is _N = N1 v+_v v f 1v2 dv. (b) If _v is small then f 1v2 is approximately constant over the interval and _N _ Nf 1v2_v. For oxygen gas 1O2 molar mass 32.0 g>mol2 at T = 300 K use this approximation to calculate the number of molecules with speeds within _v = 20 m>s of vmp . Express your answer as a multiple of N. (c) Repeat part (b) for speeds within _v = 20 m>s of 7vmp. (d) Repeat parts (b) and (c) for a temperature of 600 K. (e) Repeat parts (b) and (c) for a temperature of 150 K. (f) What do your results tell you about the shape of the distribution as a function of temperature? Do your conclusions agree with what is shown in Fig. 18.23?

University Physics with Modern Physics lessons by JJtheTutor. Designed to teach students problem solving skills, test taking skills and how to understand the concepts.