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

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You could use Bernoulli's equation to get a more precise answer, but the simpler answer to (c) is that a solution is possible.In summary, a dilution flask is a helpful tool in testing the dynamic response of a spectrophotometer. By using an exponential dilution flask, which involves continuously diluting a dye solution while measuring its absorbance, the speed and accuracy of the spectrophotometer's response can be tested. For the second question, a spherical balloon shape is assumed and a solution is possible for the problem at hand.
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## 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?

## 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.

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Bump,

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

Woopydalan said:
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.

## 1. What causes H2 to leave a balloon?

H2 gas leaves a balloon due to the principle of diffusion. The gas particles inside the balloon are constantly moving and colliding with each other, and eventually some of them will escape through the small pores in the balloon's material.

## 2. How long does it take for H2 to leave a balloon?

The rate at which H2 leaves a balloon depends on several factors such as the size and material of the balloon, the temperature and pressure of the surrounding environment, and the initial amount of H2 present in the balloon. Generally, it can take anywhere from a few hours to several days for all the H2 to leave a balloon.

## 3. Is it dangerous to inhale H2 gas from a balloon?

Inhaling H2 gas from a balloon can be dangerous as it can cause asphyxiation. H2 is an odorless and colorless gas, so it can easily displace the oxygen in the air and lead to suffocation. It is important to handle and dispose of H2-filled balloons safely to avoid any potential hazards.

## 4. Can H2 gas leave a balloon if it is tied or sealed?

Yes, H2 gas can still leave a balloon even if it is tied or sealed. As mentioned earlier, the gas particles are constantly moving and can escape through small pores in the balloon's material. Tying or sealing the balloon only slows down the rate at which H2 leaves, but it will still eventually escape.

## 5. How does the temperature affect the amount of H2 that leaves a balloon?

The temperature of the surrounding environment can affect the rate at which H2 leaves a balloon. Higher temperatures will cause the gas particles to move faster and increase the rate of diffusion, resulting in more H2 escaping the balloon. On the other hand, lower temperatures will slow down the movement of gas particles and decrease the rate of diffusion.