Pressure inside a chamber with a piston

In summary, a vertical cylinder with a tight-fitting, frictionless piston of mass 30 kg and cross-sectional area .07 m^2 contains 1 mol of an ideal gas at 395 K. The pressure inside the cylinder, taking into account atmospheric pressure, is 105,500 Pa. To find the height of the piston in equilibrium under its own weight, the downward force of the piston (294 N) and the atmospheric pressure (101,300 N/m^2) are added and divided by the area (.07 m^2) to give a final pressure of 105,500 Pa.
  • #1
alexithymia916
9
0
:mad:

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.
 
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  • #2
alexithymia916 said:
:mad:

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
 
  • #3
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 =(
 
  • #4
alexithymia916 said:
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
 
  • #5
Andrew Mason said:
You are forgetting about atmospheric pressure.

AM

ohhh
err..
how do i find that? =(
 
  • #6
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? :(
 
Last edited:
  • #7
alexithymia916 said:
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
 

1. What is pressure?

Pressure is defined as the amount of force exerted per unit area. In the case of a chamber with a piston, pressure is the force exerted by the gas molecules inside the chamber on the walls of the chamber.

2. How does pressure change with the movement of the piston?

As the piston moves, the volume of the chamber changes, causing the gas molecules inside to either spread out or become more compressed. This change in volume affects the number of collisions between the gas molecules and the chamber walls, thus altering the pressure inside the chamber.

3. What is the relationship between pressure and volume in this scenario?

According to Boyle's Law, there is an inverse relationship between pressure and volume. This means that as the volume of the chamber decreases, the pressure inside the chamber increases and vice versa, as long as the temperature and amount of gas molecules remain constant.

4. How does temperature affect pressure in a chamber with a piston?

According to Charles's Law, there is a direct relationship between temperature and pressure. This means that as the temperature of the gas molecules inside the chamber increases, the pressure also increases, and vice versa, as long as the volume and amount of gas molecules remain constant.

5. What is the ideal gas law and how does it apply to the pressure inside a chamber with a piston?

The ideal gas law is a mathematical relationship that describes the behavior of an ideal gas. It states that the product of pressure and volume is directly proportional to the temperature and the number of moles of the gas. Therefore, in a chamber with a piston, the ideal gas law can be used to calculate the pressure inside the chamber as long as the other variables are known.

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