Number of balloons that can be filled from a gas cylinder

In summary: Pressure is scalar, but the force that results on an area element ##\vec{dA}## is ##P\vec{dA}##.The net force on the balloon is zero, unless you leave a small opening and watch the balloon zoom off. But the force on each area element has to be balanced by the tension in the surface. Since each area element is a small cap, there is a net radial force from this tension.ThanksPressure is scalar, but the force that results on an area element ##\vec{dA}## is ##P\vec{dA}##.The net force
  • #1
songoku
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Homework Statement
A gas cylinder contains 4.00 × 10^4 cm^3 of hydrogen at a pressure of 2.50 × 10^7 Pa and a temperature of 290 K. The cylinder is to be used to fill balloons. Each balloon, when filled, contains 7.24 × 10^3 cm^3 of hydrogen at a pressure of 1.85 × 10^5 Pa and a temperature of 290 K. Calculate the number of balloons that can be filled from the cylinder
Relevant Equations
PV = nRT
##\frac{P_{cylinder}.V_{cylinder}}{P_{balloon}.V_{balloon}}=\frac{n_{cylinder}.R.T}{n_{balloon}.R.T}##

##\frac{n_{cylinder}}{n_{balloon}}=\frac{4 \times 10^4 \times 2.5 \times 10^7}{7.24 \times 10^3 \times 1.85 \times 10^5} \approx 746##

But the teacher said I should take the volume of gas cylinder into consideration. If I did, then the answer should be smaller.

I think I have used volume of gas cylinder into consideration in my working. What is my mistake?

Thanks
 
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  • #2
songoku said:
Homework Statement:: A gas cylinder contains 4.00 × 10^4 cm^3 of hydrogen at a pressure of 2.50 × 10^7 Pa and a temperature of 290 K. The cylinder is to be used to fill balloons. Each balloon, when filled, contains 7.24 × 10^3 cm^3 of hydrogen at a pressure of 1.85 × 10^5 Pa and a temperature of 290 K. Calculate the number of balloons that can be filled from the cylinder
Relevant Equations:: PV = nRT

##\frac{P_{cylinder}.V_{cylinder}}{P_{balloon}.V_{balloon}}=\frac{n_{cylinder}.R.T}{n_{balloon}.R.T}##

##\frac{n_{cylinder}}{n_{balloon}}=\frac{4 \times 10^4 \times 2.5 \times 10^7}{7.24 \times 10^3 \times 1.85 \times 10^5} \approx 746##

But the teacher said I should take the volume of gas cylinder into consideration. If I did, then the answer should be smaller.

I think I have used volume of gas cylinder into consideration in my working. What is my mistake?

Thanks
What are the differences in the state of the cylinder's gas between the initial state and after filling one balloon?
 
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  • #3
haruspex said:
What are the differences in the state of the cylinder's gas between the initial state and after filling one balloon?
The pressure and number of moles of the gas?
 
  • #4
songoku said:
The pressure and number of moles of the gas?
Right, the pressure is lower. How might that become a problem?
(Are these gauge pressures or absolute?)
 
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  • #5
haruspex said:
Right, the pressure is lower. How might that become a problem?
It can make the cylinder "collapse" because the inner pressure is lower than outer pressure (atmospheric pressure)?

(Are these gauge pressures or absolute?)
Absolute pressure?

Thanks
 
  • #6
songoku said:
It can make the cylinder "collapse" because the inner pressure is lower than outer pressure (atmospheric pressure)?
Before that happens it will be lower than...?
songoku said:
Absolute pressure?
I'm asking you, but since it gives the balloon pressure as about 1.85 atmospheres I would guess they are absolute.
 
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  • #7
haruspex said:
Before that happens it will be lower than...?

Lower than pressure of the balloon. So when the pressure of the gas cylinder is the same as balloon, the gas cylinder can not be used anymore to fill the balloon?

Thanks
 
  • #8
songoku said:
Lower than pressure of the balloon. So when the pressure of the gas cylinder is the same as balloon, the gas cylinder can not be used anymore to fill the balloon?

Thanks
Of course.
 
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  • #9
Thank you very much for the help haruspex
 
  • #10
Sorry I have another question

Why the gas cylinder and balloon do not "explode" even though they have pressure higher than surrounding pressure (atmospheric pressure)?

Thanks
 
  • #11
songoku said:
Sorry I have another question

Why the gas cylinder and balloon do not "explode" even though they have pressure higher than surrounding pressure (atmospheric pressure)?

Thanks
Because the container is strong enough to withstand the pressure difference. It will be under tension.
 
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  • #12
haruspex said:
Because the container is strong enough to withstand the pressure difference. It will be under tension.
Let's take balloon as example. There will be net pressure directed outwards because the inside pressure is higher than outside pressure. From ##P=\frac{F}{A}##, there will be force acting on the balloon, which is also directed outwards.

1. If we consider the balloon is perfect sphere, then the forces on all part of the sphere will cancel each other so the resultant force due to the pressure difference is zero?

2. Pressure is scalar quantity but why it seems that pressure has direction? Pressure inside a container by a gas is "outwards", pressure by atmospheric is "inwards", or pressure on top of a cylinder immersed fully in water is "downwards"?

Thanks
 
  • #13
songoku said:
Let's take balloon as example. There will be net pressure directed outwards because the inside pressure is higher than outside pressure. From ##P=\frac{F}{A}##, there will be force acting on the balloon, which is also directed outwards.

1. If we consider the balloon is perfect sphere, then the forces on all part of the sphere will cancel each other so the resultant force due to the pressure difference is zero?

2. Pressure is scalar quantity but why it seems that pressure has direction? Pressure inside a container by a gas is "outwards", pressure by atmospheric is "inwards", or pressure on top of a cylinder immersed fully in water is "downwards"?

Thanks
Pressure is scalar, but the force that results on an area element ##\vec{dA}## is ##P\vec{dA}##.
The net force on the balloon is zero, unless you leave a small opening and watch the balloon zoom off. But the force on each area element has to be balanced by the tension in the surface. Since each area element is a small cap, there is a net radial force from this tension.
Have you worked with bubbles? Let the surface tension (force per unit length) be ##\sigma## and the internal pressure be P. Consider a hemisphere radius r. The net force from the gas is ##P\pi r^2##. This is balanced by the tension around the rim, ##2\pi r\sigma##, so ##P=\frac{2\sigma}r##. That is for a single-walled bubble.
 
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  • #14
haruspex said:
Pressure is scalar, but the force that results on an area element ##\vec{dA}## is ##P\vec{dA}##.
The net force on the balloon is zero, unless you leave a small opening and watch the balloon zoom off. But the force on each area element has to be balanced by the tension in the surface. Since each area element is a small cap, there is a net radial force from this tension.
Have you worked with bubbles? Let the surface tension (force per unit length) be ##\sigma## and the internal pressure be P. Consider a hemisphere radius r. The net force from the gas is ##P\pi r^2##. This is balanced by the tension around the rim, ##2\pi r\sigma##, so ##P=\frac{2\sigma}r##. That is for a single-walled bubble.
Thank you very much haruspex
 

Related to Number of balloons that can be filled from a gas cylinder

1. How many balloons can be filled from a gas cylinder?

The number of balloons that can be filled from a gas cylinder depends on the size of the cylinder and the size of the balloons. Generally, a standard 14.9 cubic foot helium gas cylinder can fill around 50-60 9-inch balloons.

2. Can I refill a gas cylinder once it is empty?

Yes, most gas cylinders can be refilled once they are empty. However, it is important to check with the manufacturer to ensure that the cylinder is refillable and to follow proper procedures for refilling.

3. How do I calculate the number of balloons that can be filled from a gas cylinder?

To calculate the number of balloons that can be filled from a gas cylinder, you will need to know the volume of the cylinder and the volume of the balloons. Divide the volume of the cylinder by the volume of each balloon to get the approximate number of balloons that can be filled.

4. Can I use any type of gas to fill balloons from a gas cylinder?

No, it is important to use the correct type of gas for filling balloons. Helium is the most commonly used gas for filling balloons, as it is lighter than air and causes the balloons to float. Other gases, such as hydrogen or nitrogen, may be used for special effects, but should be used with caution.

5. How long will a gas cylinder last when filling balloons?

The duration of a gas cylinder when filling balloons will depend on the size of the cylinder and the size of the balloons. A standard 14.9 cubic foot helium gas cylinder can fill around 50-60 9-inch balloons. If you are filling larger balloons, the number of balloons that can be filled will be less.

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