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A cylinder of compressed Oxygen is carried on a spacecraft headed for Mars. The compressed gas cylinder has a volume of 10,000 L and is filled to a pressure of 200 atm at 273 K. The maximum pressure the cylinder can hold is 1000 atm.
The molar mass of Oxygen is 32 g/mol.
Boltzmann's constant = 1.38×10-23 J/K
Avogadro's constant = 6.02×1023 1/mol
1 L = 1000 cm3 = 0.001 m3
R = 8.31 J/mol K

(b) What is the rms velocity of the oxygen molecules in the cylinder at it's maximum temperature?


for temperature i got 1365 can't figure this out

  • physics -

    There is a lot of unecessary information in ths problem. It doesn't matter what the volume is or or if it is going to Mars or Peoria.

    The maximum pressure the tank can withstand does matter. If the tank pressure can only reach 1000 atm and it is 200 atm at 273K, then the temperature cannot exceet 5*273 = 1365 K. You got that part right.

    The formula for the rms velocity of atoms and molecules of a gas is:

    V = sqrt(3 k T/m)
    where m is the mass of an O2 molecule,
    32*10^-3 kg/6.02*10^23 = 5.32*10^-26 kg

    Use that formula, with T = 1365, to get the max rms velocity.

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