Consider the Universe to be an adiabatic expansion of atomic hydrogen gas. (a) U
ID: 1266828 • Letter: C
Question
Consider the Universe to be an adiabatic expansion of atomic hydrogen gas.
(a) Use the ideal gas law and Equation 12.8a to show that TV? - 1 = C, where C is a constant. (Do this on paper. Your instructor may ask you to turn in this work.)
(b) The current Universe extends at least 15 billion light-years in all directions (1.4 ? 1026 m), 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 2.0 cm. (For this calculation, assume the Universe is spherical. Use ? = 1.67.)
Your response differs significantly from the correct answer. Rework your solution from the beginning and check each step carefully. K
This question is the exact same one in the text book but its not the same answer! why?!? Please help!
Explanation / Answer
a)
PV^? = constant
and,
PV = nRT
P = constant * T / V
substituting :
constant * (T / V ) * V^? = constant
? TV^?-1 = constant
b)
Atomic Hydrogen gas : ? = 1.4
T1V1^0.4 = T2V2^0.4
Since V ? R^3
T1 = T2 * (V2/V1)^0.4 = 2.7 * (1.4*10^26 / 0.02)^3*0.4
T1 = 2.7 * (0.7 * 10^28)^1.2
= 7 * 10^33 K