# Exploring an Expandable Gas Cylinder

• Touchme
In summary, this conversation discusses the calculation of volume and pressure in an expandable cylinder filled with gas and connected to a spring with a force constant. The gas law, PV = nRT, is used to determine the force constant, and the equation for pressure, P = F/A, is used to calculate the displacement of the piston. There is a discrepancy in the final answer and further suggestions or corrections are requested.
Touchme

## Homework Statement

An expandable cylinder has its top connected to a spring with force constant 2.00 103 N/m. (See Fig. P10.58.) The cylinder is filled with 6.00 L of gas with the spring relaxed at a pressure of 1.00 atm and a temperature of 20.0°C.

I searched for a similar question however I didnt understand it. Maybe it was the calculation error. Someone help me...

## Homework Equations

PV = nRT
[PV/T]i = [PV/T]f
Volume of cylinder = Ah

## The Attempt at a Solution

First I convert my units. Initial state: 101325 Pa, 293 K, and 0.006 m^3
I determined the constant by using the gas law PV/T. (101325)(0.006)/293 = 2.0749 [(Nm^2)/K].
After the temperature is increased to 503 K (273+230), the piston rises and the volume changes. The new volume is 0.006 + Ah = 0.006 + 0.01h. The pressure is equal to P = F/A. F is the force constant times dispalcement (h), which is 2000 N/m. P = 2000/0.01 = 200000h N/m^2.
Putting everything together we get
2.0749 = (200000h)(0.006+0.01h)/503

The answer h = 0.482 m or 48.2 cm is incorrect. Any suggestion or corrections. Thank you.

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Touchme said:

## Homework Statement

An expandable cylinder has its top connected to a spring with force constant 2.00 103 N/m. (See Fig. P10.58.) The cylinder is filled with 6.00 L of gas with the spring relaxed at a pressure of 1.00 atm and a temperature of 20.0°C.I searched for a similar question however I didnt understand it. Maybe it was the calculation error. Someone help me...

## Homework Equations

PV = nRT
[PV/T]i = [PV/T]f
Volume of cylinder = Ah

## The Attempt at a Solution

First I convert my units. Initial state: 101325 Pa, 293 K, and 0.006 m^3
I determined the constant by using the gas law PV/T. (101325)(0.006)/293 = 2.0749 [(Nm^2)/K].
After the temperature is increased to 503 K (273+230), the piston rises and the volume changes. The new volume is 0.006 + Ah = 0.006 + 0.01h. The pressure is equal to P = F/A. F is the force constant times dispalcement (h), which is 2000 N/m. P = 2000/0.01 = 200000h N/m^2.
Putting everything together we get
2.0749 = (200000h)(0.006+0.01h)/503

The answer h = 0.482 m or 48.2 cm is incorrect. Any suggestion or corrections. Thank you.

You have to develop the equation for pressure:

$$P_f = P_i + kh/A = nRT_f/V_f$$

Since $P_i = nRT_i/V_i$, and $V_f = V_i + Ah$

you should be able to work that out for h.

AM

I would suggest double-checking your calculations and units to ensure accuracy. It is also important to consider the ideal gas law and how it applies to the situation. Additionally, it may be helpful to draw a diagram to visualize the problem and see if there are any other factors that need to be taken into account. If you are still having trouble, I recommend seeking guidance from a teacher or classmate for further assistance.

## 1. What is an expandable gas cylinder?

An expandable gas cylinder is a storage vessel that can hold compressed gas and has the ability to increase its volume to accommodate more gas as it is being filled. This expansion is achieved through the use of a flexible membrane or a piston.

## 2. How does an expandable gas cylinder work?

An expandable gas cylinder works by utilizing the physical properties of gases. As gas molecules are compressed and pushed closer together, they exert pressure on the walls of the cylinder. This pressure causes the cylinder to expand, allowing more gas to be stored.

## 3. What are the common uses of expandable gas cylinders?

Expandable gas cylinders have a variety of uses, including storing and transporting compressed gases such as oxygen, nitrogen, and carbon dioxide. They are also used in industries such as healthcare, manufacturing, and aerospace for various applications.

## 4. How are expandable gas cylinders tested for safety?

Expandable gas cylinders undergo rigorous testing to ensure their safety. This includes pressure tests, leak tests, and burst tests. These tests are performed by trained professionals and must meet strict standards set by regulatory agencies.

## 5. How should expandable gas cylinders be handled and stored?

Expandable gas cylinders should be handled and stored with caution. They should be kept in a well-ventilated area away from heat, flames, and sources of ignition. It is also important to follow proper storage and transport guidelines to avoid potential hazards.

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