Suppose the Universe is considered to be an ideal gas of hydrogen atoms expandin

Question

Suppose the Universe is considered to be an ideal gas of hydrogen atoms expanding adiabatically. (a) If the density of gas in the Universe is one hydrogen atom per cubic meter, calculate the number of moles per unit volume (n/V). (b) Calculate the pressure of the Universe, taking the temperature of the Universe as 2.7 K. (c) If the current radius of the Universe is 15 billion light-years (1.4 x 10 raise to the 26 power meters), find the pressure of the Universe when it was the size of a nutshell, with radius 2.0 x 10 raised to the power o -2 meters. Be careful: Calculator overflow can occur.

Explanation / Answer

one hydrogen atom per cubic meter. so Number of moles per unit volumne. 1/6.023e23=1.66e-24(n/m3). b). P*V=nRT. so P=nRT/V=3.7e-23(K). because P=nRT/V so P*V=const. radius power by three is directly proportional to volume. so P*r^3=const. so P'=P0*r0^3/r'^3=1.278e61(Pa)

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