How Does Temperature Affect Gas Pressure in a Sealed Cylinder?

[shaiqbashir]

Hi Guys!

please help me in this problem. and also tell me the correct answer which u have calculated. the prob is as under:

"A gas is confined in a steel cylinder at 20 degree celcius and at a pressure of 5 atm.

a) if the cylinder is surrounded by boiling water and allowed to come to the thermal equilibrium, how great will the gas pressure be?

b) if the gas is then allowed tp escape until the pressure is again 5 atm, what fraction of the original gas (by weight) will escape?

c) if the temperature of the remaining gas in the cylinder is returned to 20 degree celsius, what will be its final pressure?"

Thanks in advance

 

[Astronuc]

A student must show some work. Assuming 1 atm of pressure for the boiling water - at what temperature will the water be when boiling?

Then a) adjust the pressure from 20°C to the water boiling temperature (don't forget to use absolute temperatures).

Hint: PV = nRT, so at constant volume P1/T1=P2/T2.

Refer to - http://hyperphysics.phy-astr.gsu.edu/hbase/kinetic/idegas.html#c1 - and read the frames.

 

[shaiqbashir]

Astronuc that is what i have solved too!
but i want help in (b) and (c) parts where we have to find weight. This is the real problem for me!

Pressure and volume are inversly propotional to each other. if the gas escapes, it means its volume decreases so why the pressure is also decreasing> Please explain me the scenario in detail

 

[Rocketa]

b) if the gas is then allowed tp escape until the pressure is again 5 atm, what fraction of the original gas (by weight) will escape?

what means tp escape?

You already know initial pressure in this case from question a, right? Then you need to find what the portion of the gas will occupy the cylinder after pressure drop to P2=5atm

P1V1=P2V2 V2 is the tank volume and V1 is what you need to find.

Pressure decrease because PV=constant. V1 doesn't equal to V2.

c) if the temperature of the remaining gas in the cylinder is returned to 20 degree celsius, what will be its final pressure?"

P2V2=RT2
P3V2=RT3 find P3

 

[shaiqbashir]

Thanks a lot Rocketa! now i understood the question just tell me if i have made it correctly.

The answer of (b) part is

V1=0.87987V2

and the answer of (c) part is

P3=4.3999 atm aprrrox..

Thanks a lot in advance