How Long Will It Take to Safely Deflate a Balloon to Fit Through a Door?

[member 392791]

Homework Statement

To test the dynamic response of an inline or flow-through spectrophotometer, it is helpful to use an exponential dilution flask upstream of the photometer. The effluent from a small continuous, stirred tank (i.e., a flask) is fed to the photometer. Initially, the tank is filled with a dilute dye at concentration C. Then, clear solvent (i.e., containing no dye) is fed to the flask while maintaining the same inlet and outlet flow rates. If the transmitted absorbance measured by the photometer (i.e. minus the logarithm of the intensity) is linear with dye concentration, find an expression for the spectrophotometer absorbance, A, in terms of a steady flow rate Q, and the steady volume of liquid in the flask, V. Explain why the device is called exponential dilution flask and why it is useful in testing the dynamic behavior of the spectrophotometer

An advertising firm wants to get a special inflated sign out of a warehouse. The sign
is 20 ft in diameter and is filled with H2 at 15 psig. Unfortunately, the door frame to
the warehouse permits only 19 ft to pass. The maximum rate of H2 that can be safely
vented from the balloon is 5 ft3/min (measured at room conditions). How long will it
take to get the sign small enough to just pass through the door?
(a) First assume that the pressure inside the balloon is constant so that the flow rate
is constant.
(b) Then assume the amount of amount of H2 escaping is proportional to the volume
of the balloon, and initially is 5 ft3/min.
(c) Could a solution to this problem be obtained if the amount of escaping H2 were
proportional to the pressure difference inside and outside the balloon?

Homework Equations

The Attempt at a Solution

Sorry for posting 2 questions on one thread, it's just for the 1st question I am unsure about what they mean about the usefulness of a dilution flask in testing the dynamic behavior of a spectrophotometer, no idea what that means, nor how being a dilution flask would have anything to do with it.

EDIT: Upon reading, I am wondering if it's used because the change is concentration happens so rapidly since it is exponential, thus it is able to test how quickly the spectrophotometer is able to pick up the changes in concentration via absorption. Is this right?For question 2, I am stuck on park C. Not sure how to go about showing whether or not there could be a solution. I'm guessing there is a solution, it seems like one could model that sort of behavior. Also for this problem I assumed the balloon is a sphere, although the problem statement didn't really indicate the shape of the balloon.

 

[member 392791]

Bump,

any idea where to start with part C? Or even if A and B are correct

 

[NascentOxygen]

1st question I am unsure about what they mean about the usefulness of a dilution flask in testing the dynamic behavior of a spectrophotometer, no idea what that means, nor how being a dilution flask would have anything to do with it.

EDIT: Upon reading, I am wondering if it's used because the change is concentration happens so rapidly since it is exponential, thus it is able to test how quickly the spectrophotometer is able to pick up the changes in concentration via absorption. Is this right?

Concentration won't change rapidly. The initial concentration of dye is C molecules/litre, say. After half the tank has been drained off and replaced by clear solution, and all the while stirred, the concentration will be C/2 molecules/litre. This "halving" of the concentration keeps happening in a fixed time period while the fixed flow rate is maintained. That is the exponential graph, the concentration of dye vs. time. It's a decaying exponential.

(Here is a data set that's an example of a decaying exponential, too, for fixed x intervals:

y: 4096, 2048, 1024, 512, 256, 128, 64, 32, 16, 8, 4 )

For question 2, I am stuck on park C. Not sure how to go about showing whether or not there could be a solution. I'm guessing there is a solution, it seems like one could model that sort of behavior. Also for this problem I assumed the balloon is a sphere, although the problem statement didn't really indicate the shape of the balloon.

A spherical balloon shape is perfectly appropriate. The solution to a first order differential equation is involved.