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 - drwls, Thursday, May 6, 2010 at 9:01pm
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.
I DID THIS
(sqrt(34 029.45) / 5.32) * (10^(-26))
and i got a freaky number like below
3.46749491 × 10-25
but that's not the right answer
i got 34029.45 by multiplying 1365x8.31x3
whats wrongg??
I don't follow your sqrt calculation at all. in the sqrt (3*k*Temp/m) I don't see that at all.
strt(3 * k=8.31 * T=1365)/ m = 5.32*10^-26
Looks like you are using R (the gas constant) where you should be using k (the Boltzmann constant.
oo ok let me try that also can you tell me the distinction like when to use gas constant and boltzmann constant
You ought to know the constants in an equation. It is similar to recognizing your wife when in a group of ladies, I recommend you commit her face to memory...otherwise, big errors will continue to occur.
To calculate the root mean square (rms) velocity of the oxygen molecules in the cylinder at its maximum temperature, you are on the right track. Let's break down the calculation step by step.
1. First, let's calculate the mass of an oxygen molecule (O2):
The molar mass of oxygen is given as 32 g/mol, so the mass of one oxygen molecule is:
Mass of O2 molecule = (32 g/mol) / (6.02 × 10^23 molecules/mol) = 5.32 × 10^-26 kg
2. Now, we can use the formula for rms velocity:
V = sqrt(3kT/m)
Where:
V = rms velocity
k = Boltzmann's constant = 1.38 × 10^-23 J/K
T = Temperature in Kelvin = 1365 K (as you correctly calculated)
m = mass of an oxygen molecule = 5.32 × 10^-26 kg
3. Substitute the values into the formula and solve:
V = sqrt(3 * (1.38 × 10^-23 J/K) * (1365 K) / (5.32 × 10^-26 kg))
Calculating the value inside the square root:
(3 * (1.38 × 10^-23 J/K) * (1365 K)) / (5.32 × 10^-26 kg) = 34.03 m^2/s^2
Taking the square root:
V = sqrt(34.03 m^2/s^2) ≈ 5.83 m/s
So the rms velocity of the oxygen molecules in the cylinder at its maximum temperature is approximately 5.83 m/s.