A latex balloon, wall thickness 3.091 x 10-4 m, contains helium at a concentration of 0.35 kg m-3. Under these conditions the total surface area of the balloon is 0.57 m2. The diffusion coefficient of He in latex at room temperature is 4.9 x 10-9 m2s-1. Calculate the rate of helium effusion (in g/hr) from the balloon.
Fick’s Law
M= -D•(Δρ/Δx)•A,
where
M = m/t = mass flux [kg/s],
D= 4.9•10 ⁻⁹ m ²/s is the diffusion coefficient (diffusivity) [m²/s],
Δρ/Δx is the gradient of density [kg/m⁴],
A is the area [m²].
M= - 4.9•10⁻⁹•(0 - 0.35)/3.091•10⁻⁴)•0.88 =
4.9•10⁻⁹•0.35•0.88/3.091•10⁻⁴=
=4.88•10⁻⁶ kg/s= 17.58 g/hr
A latex balloon, wall thickness 3.091 x 10-4 m, contains helium at a concentration of 0.42 kg m-3. Under these conditions the total surface area of the balloon is 0.46 m2. The diffusion coefficient of He in latex at room temperature is 4.9 x 10-9 m2s-1. Calculate the rate of helium effusion (in g/hr) from the balloon.
To calculate the rate of helium effusion from the balloon, you can use Fick's Law of Diffusion, which states that the rate of diffusion is directly proportional to the surface area and concentration difference, and inversely proportional to the thickness of the material.
The formula can be written as:
Rate of diffusion = Diffusion coefficient * Surface area * (Concentration difference / Thickness)
First, convert the units to the appropriate SI units:
- The diffusion coefficient is 4.9 x 10^-9 m^2/s.
- The surface area is 0.57 m^2.
- The concentration of helium is 0.35 kg/m^3.
- The thickness of the wall is 3.091 x 10^-4 m.
Next, calculate the concentration difference. Assuming there is no helium outside the balloon, the concentration difference would just be the concentration inside the balloon:
Concentration difference = 0.35 kg/m^3
Now, plug the values into the formula and solve for the rate of diffusion:
Rate of diffusion = (4.9 x 10^-9 m^2/s) * (0.57 m^2) * (0.35 kg/m^3 / (3.091 x 10^-4 m))
The units in the formula simplify to give the rate of diffusion in kg/s. To convert it to grams per hour, you need to multiply by the appropriate conversion factors:
Rate of diffusion (g/hr) = (Rate of diffusion (kg/s)) * (3600 s/hr) * (1000 g/kg)
After performing the calculation, you will get the rate of helium effusion from the balloon in grams per hour.
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