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spherical23
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Homework Statement
14 grams of Nitrogen at 20 degrees Celsius in 1 atmosphere of pressure is compressed to a pressure of 20 atmospheres. What is its final temperature and what is the work done on the gas if the process is adiabatic? Obtain the compression ratio (i.e. Vmax/Vmin). How much heat comes in or leaves the gas? What is the ratio of Pmax/Pmin? Show this change on a P-V graph.
Homework Equations
PV = NkT
PinitialVinitial[tex]\gamma[/tex] = PfinalVfinal[tex]\gamma[/tex]
VinitialTinitial[tex]3/2[/tex] = VfinalTfinal[tex]3/2[/tex]
W = -[((PinitialVinitial[tex]\gamma[/tex])/(1-[tex]\gamma[/tex]))(Vfinal(1-[tex]\gamma[/tex]) - Vinitial(1-[tex]\gamma[/tex]))
The Attempt at a Solution
14 grams of Nitrogen = 1 atom
Tinitial = 20 degrees Celsius = 293 Kelvin
Tfinal = ?
Pinitial = 1 atm = 1.013 * 105 Pa (1 Pa = 1 N/m2)
~
PinitialVinitial = NkTinitial
(1.013 * 105 N/m2)Vinitial = 1(1.381 * 10-23 Nm/K)(293K)
Vinitial [tex]\approx[/tex] 4 * 10-26
~
PinitialVinitial[tex]\gamma[/tex] = PfinalVfinal[tex]\gamma[/tex]
(1.013 * 105 N/m2)(4 * 10-26) = (20 atm)(1.013 * 105 N/m2)Vfinal[tex]\gamma[/tex]
Vfinal = (4 * 10-26 m3) [tex]\sqrt[5]{[1.013 * 105 N/m2) / ((20 atm)(1.013 * 105 N/m2))]3}[/tex]
where [tex]\gamma[/tex] = 5/3
Vfinal [tex]\approx[/tex] 6.6 * 10-29 m3
Okay... I'm not done yet, but I am going to submit this to check out how my latex reference skills are working out. This is tedious.