Physics, 29.01.2020 06:59 michellemonroe012305
Newtonian cosmology 1. in class, we solved the friedmann equation for the critical case, where the constant of integration was set to k 0; this resulted in the einstein-de sitter model, where a ox t2/3 now, let us consider the closed case (k 1), where the universe starts with a big bang, reaches a maximum expansion, turns around, and eventually ends in a big crunch. for the closed model, it is convenient to write the friedmann equation as follows: 8t g po (a1) 3 where po is the present-day mass density a. show that this equation can be solved with the following parametric expressions: a= sin a and a (a sin a cos a) t where a is a "development angle", such that a = 0 corresponds corresponds to the point of maximum expansion ("turn-around"), and a crunch to the big bang, a = mt 2t to the big find an expression for the constant a b. plot this solution, showing the scale factor on the y-axis, and time on the x-axis. assuming po = 5 x 10-29 g cm, show time in units of gyr. (recall that the scale factor is dimensionless.) c. what is the total duration of such a universe? ie, what is the time elapsing between big bang and big crunch (in units of gyr)? d. show that at early times, i. e., for small development angles a, the closed solution discussed here appoximately approaches the einstein-de sitter scaling (a ox t2/3). to do this, taylor expand (in a) the parametric expressions in part a above.
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Clothing made of several thin layers of fabric with trapped air in between, often called ski clothing, is commonly used in cold climates because it is light, fashionable, and a very effective thermal insulator. so it is no surprise that such clothing has largely replaced thickand heavy old-fashioned coats. (a) consider a jacket made of five layers of 0.1-mm-thick synthetic fabric (k = 0.13 w/m·°c) with 1.5-mm-thick air space (k = 0.026 w/m·°c) between the layers. assuming the inner surface temperature of the jacket to be 28°c and the surface area to be 1.25 m2, determine the rate of heat loss through the jacket when the temperature of the outdoors is 0°c and the heat transfer coefficient at the outer surface is 25 w/m2·°c. (b) what would your response be if the jacket is made of a single layer of 0.5-mm-thick synthetic fabric? what should be the thickness of a wool fabric (k = 0.035 w/m·°c) if the person is to achieve the same level of thermal comfort wearing a thick wool coat instead of a five-layer ski jacket?
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Newtonian cosmology 1. in class, we solved the friedmann equation for the critical case, where the c...
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