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)

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