A balloo n, initially at a volume of 0.3 cm 3 and filled with an ideal gas at a

Question

A balloon, initially at a volume of 0.3 cm3 and filled with an ideal gas at a pressure of 1 atm, is to be filled by flowing in helium at a rate of 1 cm3/s and a pressure of 25 atm. The balloon will expand as helium enters to maintain a pressure inside the balloon of 1 atm. Helium may be treated as an ideal gas, and both the flow in and the temperature in the balloon are maintained at 25 °C.
b) Once filled to a volume of 1200 cm3, the balloon leaks due to the diffusion of helium through the balloon material. The flux of helium across the balloon surface can be expressed as kC, where C is the concentration of gas inside the balloon and k is a mass transfer coefficient with a value of 1x10-7 cm/s. Determine how long it takes for the balloon to shrink to a volume of 600 cm3. You may treat the balloon as spherical. Useful expressions (where r is the sphere radius): Volume of a sphere = 4/3 p r3 Area of a sphere = 4 p r2 dr3/dr = 3r2 c) Write the mole balance that would be used to re-examine the filling process if the diffusion of helium out of the balloon was considered during filling. Do you anticipate the filling time changing substantially due to helium diffusion? You do not need to resolve for the filling time. A balloon, initially at a volume of 0.3 cm3 and filled with an ideal gas at a pressure of 1 atm, is to be filled by flowing in helium at a rate of 1 cm3/s and a pressure of 25 atm. The balloon will expand as helium enters to maintain a pressure inside the balloon of 1 atm. Helium may be treated as an ideal gas, and both the flow in and the temperature in the balloon are maintained at 25 °C.
b) Once filled to a volume of 1200 cm3, the balloon leaks due to the diffusion of helium through the balloon material. The flux of helium across the balloon surface can be expressed as kC, where C is the concentration of gas inside the balloon and k is a mass transfer coefficient with a value of 1x10-7 cm/s. Determine how long it takes for the balloon to shrink to a volume of 600 cm3. You may treat the balloon as spherical. Useful expressions (where r is the sphere radius): Volume of a sphere = 4/3 p r3 Area of a sphere = 4 p r2 dr3/dr = 3r2 c) Write the mole balance that would be used to re-examine the filling process if the diffusion of helium out of the balloon was considered during filling. Do you anticipate the filling time changing substantially due to helium diffusion? You do not need to resolve for the filling time.
b) Once filled to a volume of 1200 cm3, the balloon leaks due to the diffusion of helium through the balloon material. The flux of helium across the balloon surface can be expressed as kC, where C is the concentration of gas inside the balloon and k is a mass transfer coefficient with a value of 1x10-7 cm/s. Determine how long it takes for the balloon to shrink to a volume of 600 cm3. You may treat the balloon as spherical. Useful expressions (where r is the sphere radius): Volume of a sphere = 4/3 p r3 Area of a sphere = 4 p r2 dr3/dr = 3r2 c) Write the mole balance that would be used to re-examine the filling process if the diffusion of helium out of the balloon was considered during filling. Do you anticipate the filling time changing substantially due to helium diffusion? You do not need to resolve for the filling time. b) Once filled to a volume of 1200 cm3, the balloon leaks due to the diffusion of helium through the balloon material. The flux of helium across the balloon surface can be expressed as kC, where C is the concentration of gas inside the balloon and k is a mass transfer coefficient with a value of 1x10-7 cm/s. Determine how long it takes for the balloon to shrink to a volume of 600 cm3. You may treat the balloon as spherical. Useful expressions (where r is the sphere radius): Volume of a sphere = 4/3 p r3 Area of a sphere = 4 p r2 dr3/dr = 3r2 c) Write the mole balance that would be used to re-examine the filling process if the diffusion of helium out of the balloon was considered during filling. Do you anticipate the filling time changing substantially due to helium diffusion? You do not need to resolve for the filling time.

Explanation / Answer

long it takes for the balloon to shrink = (1200 - 600) * 4/3 * 3.14 * 0.0053/(1 * 10-7)

                                                          = 3140 sec

                                                           = 52.33 minutes

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