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.

Suppose the Universe is considered to be an ideal gas of hydrogen atoms expanding adiabatically. If the density of the gas in the Universe is one hydrogen atom per cubic meter, calculate the number of moles per unit volume (n/V). Calculate the pressure of the Universe, taking the temperature of the Universe as 2.7 K. If the current radius of the Universe is 15 billion light-years (1.40 Times 1026 m), find the pressure of the Universe when it was the size of a nutshell, with radius 1.80 Times 10-2 m. (Use ? = 1.67.) Be careful: calculator overflow can occur. (To minimize calculator error, simplify your calculation completely, including exponents, before entering it in your calculator. Use the calculator on your computer if necessary.) Your response differs significantly from the correct answer. Rework your solution from the beginning and check each step carefully. Pa

Explanation / Answer

v1 = (4/3)*pi*1.8^3*10^-6
v2 = (4/3)*pi*1.4^3*10^78

P1*V1^gamma = P2*V2^gamma

P1 = P2*(V2/V1)^gamma

   = 3.73*10^-23*(1.4^3*10^78/(1.8^3*10^-6)^1.67

= 1.058998*10^(117.28) pa

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