600ml container with 1200ml of air. PSI?

Question

I have a sealed container with a pressure gauge on it. The containers capacity is 600ml. If it has 600ml of air in it, the gauge will read 0 because the outside pressure is equal to the pressure inside. If I add more air to the container (compressing the air inside it) until it contains 1200ml of air, what will the pressure gauge read?

Thanks

Answer 1

It should read the pressure of the outside air. I assume you mean that the vessel contains 1200 ml of outside air compressed into 600ml.

Answer 2

Start with the ideal gas law... PV=nRT.

V= constant at 600ml

R= constant- by definition

T= Constant- not really true since the temp will go up as the gas is compressed, but will suffice for right now... if you assume that the container is not insulated, then the gas temp will finally cool down to room temperature, so assuming the T=constant after some elapsed time x is acceptable

So P is proportional to n, where n= number of moles of gas

you can calculate the number of moles of gas

.6 liters x 22.4 moles/liter= 13.44 moles

1.2 liters x 22.4 moles/liter= 26.88 moles

Since the number of moles doubled, the pressure doubled

the initial pressure= 0 psig or 14.7 psiabsolute

2xP= 29.4 psia, or 14.7 psig