Pressure inside a chamber with a piston

[alexithymia916]

Homework Statement

A vertical cylinder of cross-sectional area .07 m^2 is fitted with a tight-fitting, frictionless piston of mass 30 kg. The acceleration of gravity is 9.8 m/s^s. If there are 1 mol of an ideal gas in the cylinder at 395 K, find the pressure inside the cylinder. (Assume that the system is in equilibrium.) Answer in units of Pa.

At what height will the piston be in equilibrium under its own weight? Answer in units of m.

Homework Equations

PV=nRT
P=Pressure
V=Volume
T=Temperature
n=# of moles
R (universal)= 8.31 J/mol/K

The Attempt at a Solution

I have no idea... =(
Volume isn't given.. and I don't know how to factor in the weight of the piston on the cylinder.. And please do not ask me to refer to my textbook, this is a summer assignment and we don't have any textbooks to use.

 

[Andrew Mason]

Homework Statement

A vertical cylinder of cross-sectional area .07 m^2 is fitted with a tight-fitting, frictionless piston of mass 30 kg. The acceleration of gravity is 9.8 m/s^s. If there are 1 mol of an ideal gas in the cylinder at 395 K, find the pressure inside the cylinder. (Assume that the system is in equilibrium.) Answer in units of Pa.

At what height will the piston be in equilibrium under its own weight? Answer in units of m.

Homework Equations

PV=nRT
P=Pressure
V=Volume
T=Temperature
n=# of moles
R (universal)= 8.31 J/mol/K

The Attempt at a Solution

I have no idea... =(
Volume isn't given.. and I don't know how to factor in the weight of the piston on the cylinder.. And please do not ask me to refer to my textbook, this is a summer assignment and we don't have any textbooks to use.

What is the total upward force on the piston? So what is the downward force on the air in the cylinder if the piston does not move? What is the force/area (pressure) of the piston on the air in the cylinder? (hint: you don't need to know the temperature or volume to do this part of the question). In the second part, at this pressure and temperature, what is the volume of the air? Figure out the height from that.

AM

 

[alexithymia916]

Okay well using what you said above.. (i did something similar to that in the first place but the answer was incorrect...)
[i submit the answers online for credit and i have 2 attempts of getting the right answer]
f=ma
so
30 kg * 9.8 m/s^s
= 294 N of force from the piston working on the ideal gas
and therefore 294 N of force from the ideal gas working on the piston
294 N/.07 m^s= 4200 Pa
and somehow when i submit that it says its incorrect =(

 

[Andrew Mason]

Okay well using what you said above.. (i did something similar to that in the first place but the answer was incorrect...)
[i submit the answers online for credit and i have 2 attempts of getting the right answer]
f=ma
so
30 kg * 9.8 m/s^s
= 294 N of force from the piston working on the ideal gas
and therefore 294 N of force from the ideal gas working on the piston
294 N/.07 m^s= 4200 Pa
and somehow when i submit that it says its incorrect =(

You are forgetting about atmospheric pressure.

AM

 

[alexithymia916]

You are forgetting about atmospheric pressure.

AM

ohhh
err..
how do i find that? =(

 

[alexithymia916]

ok well i solved it but its still wrong...
i got 1 atm as the average value of atmospheric pressure
which is
101300 N/m^2
so i set up a proportion so it should be
7091 N/m^2
or
7091 Pa
+ the 4200 Pa from above
which is
11291 Pa..
which is still wrong? :(

 

[Andrew Mason]

ok well i solved it but its still wrong...
i got 1 atm as the average value of atmospheric pressure
which is
101300 N/m^2
so i set up a proportion so it should be
7091 N/m^2
or
7091 Pa
+ the 4200 Pa from above
which is
11291 Pa..
which is still wrong? :(

Pressure is force / area. Either you just add the atmospheric pressure to the pressure from the piston (101,300 + 4200 = 105,500) or you convert the atmospheric pressure on the piston into a force (which gives you 7091 Newtons) and add it to the downward force of the piston (294 N) and divide that by the area (.07 m^3) to give 105,500 Pa.

AM