# Pressure Half-Life: 2L vs. 5L Containers

• Seneka
In summary, The time it takes to reduce the pressure in a five litre container from atmospheric pressure to 1/8th of atmospheric pressure is 150 seconds. This is because the flow rate is proportional to the pressure difference, meaning a larger container will take longer to reduce the pressure. This can be seen in the example of filling a jug versus a bath from the same tap.
Seneka

## Homework Statement

A two litre sealed container is filled with air at atmospheric pressure. It is connected to a vacuum pump which can pump air at a flow rate that is proportional to the difference in pressure within the container to the pressure outside. This tells us that the pressure drops exponentially with time. If it takes 20 seconds for the pressure in the container to halve, how long would it take to reduce the pressure in a five litre container from atmospheric pressure to 1/8 th of atmospheric pressure
A. 48 s
B. 150 s
C. 200 s
D. 250 s

## Homework Equations

To halve the pressure takes 20 s, ¼ takes a further 20 s and then to 1/8 takes another 20 s. This is 60 s in total; 2½ times the volume will take 150 seconds.

3. The Attempt at a Solution [/B]

Since the pressure difference is the same and the flow rate is proportional to the difference in pressure which is the same for both why can't it just be 60 seconds for the 5 litre container too?
Whys there a linear relationship between the volume and the half life?

The flow rate is the same but the volume is larger so it takes longer.

How long does it take to fill a jug compared to a bath from same tap.

## 1. What is Pressure Half-Life?

Pressure Half-Life is a term used to describe the time it takes for a gas to reach half of its original pressure in a container. It is a measure of the rate at which a gas is released from a container.

## 2. What is the difference between 2L and 5L containers in terms of Pressure Half-Life?

The main difference between 2L and 5L containers in terms of Pressure Half-Life is the volume of gas each container can hold. A larger container (5L) will have a longer Pressure Half-Life compared to a smaller container (2L) because it has a larger volume of gas that needs to be released.

## 3. How is Pressure Half-Life affected by temperature?

The Pressure Half-Life of a gas is directly affected by temperature. As temperature increases, the molecules in the gas have more kinetic energy and collide with the walls of the container more frequently, leading to a shorter Pressure Half-Life. Conversely, a decrease in temperature will result in a longer Pressure Half-Life.

## 4. Can the material of the container affect Pressure Half-Life?

Yes, the material of the container can have an impact on Pressure Half-Life. Materials with lower permeability, such as glass, will have a longer Pressure Half-Life compared to materials with higher permeability, such as plastic. This is because gas molecules can escape more easily through materials with higher permeability.

## 5. How is Pressure Half-Life measured?

Pressure Half-Life can be measured by monitoring the pressure inside the container over time and recording the time it takes for the pressure to reach half of its original value. This can be done using a pressure gauge or a data logger connected to the container.

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