A gas cylinder holds .10 mol of O_2 at 150 degrees Celsius and a pressure of 3.0

Question

A gas cylinder holds .10 mol of O_2  at  150 degrees Celsius and a pressure of 3.0atm. The gas expands adiabatically until the pressure ishalved. Questions A) what is the final volume in meters cubed? (m^3) B)What is the final temperature in dregrees Celsius? A gas cylinder holds .10 mol of O_2  at  150 degrees Celsius and a pressure of 3.0atm. The gas expands adiabatically until the pressure ishalved. Questions A) what is the final volume in meters cubed? (m^3) B)What is the final temperature in dregrees Celsius?

Explanation / Answer

Given no . of moles , n = 0.1 temperature , T = 150 oC = 1560 + 273 = 423 K Pressure , P = 3 atm We know that PV = nRT Where V = Volume = ? R = gas constant = 0.0821 L atm / mol - K Plug the values we get V = nRT / P                                      = 1.1576 L                                       =1.1576 * 10^-3m^3                  Since 1 L = 10^-3 m^3 (a) For an adiabatic process PV =constant = ration of specific heats = 1.4 for diatomicgases PV = P'V' P = 3 atm P' = 3/2 = 1.5 atm V = 1.1576 * 10^-3 m^3 V' = ? Plug the values we get V' (b) TV -1 = T'V' -1 T = 423 K T ' = ? V = 1.1576 * 10^-3 m^3    V' = obtained in the case (a) Plug the values we get T'

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