Answered: Consider the Universe to be spherical,…

College Physics

10th Edition

ISBN:9781285737027

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter12: The Laws Of Thermodynamics

Section: Chapter Questions

Problem 28P: Suppose the Universe is considered to be an ideal gas of hydrogen atoms expanding adiabatically. (a)...

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Consider the Universe to be spherical, mostly hydrogen gas molecules undergoing adiabatic expansion over its lifetime.

a. Using the ideal gas law and properties of adiabatic processes show T V γ − 1= C where C is a constant.

b. The current Universe extends at least 15 billion light-years in all directions (r = 1.4 x 1026m), and the current temperature of the Universe is 2.7 K. Estimate the temperature of the Universe when it was the size of a nutshell, with a radius of 2 cm.

c. If the density of the gas in the Universe, N/V, is one hydrogen atom per cubic meter, calculate the current pressure of the Universe.

d. Estimate the pressure of the Universe when it was the size of a nutshell. (You may get a calculator overflow error)

Definition Definition Any of various laws that describe the ways in which volume, temperature, pressure, and other conditions correlate when matter is in a gaseous state. At a constant temperature, the pressure of a particular amount of gas is inversely proportional with its volume (Boyle's Law) In a closed system with constant pressure, the volume of an ideal gas is in direct relation with its temperature (Charles's Law) At a constant volume, the pressure of a gas is in direct relation to its temperature (Gay-Lussac's Law) If the volume of all gases are equal and under the a similar temperature and pressure, then they contain an equal number of molecules (Avogadro's Law) The state of a particular amount of gas can be determined by its pressure, volume and temperature (Ideal Gas law)

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