# Pressure half life

## 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?

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