Solving a Vertical Cylinder Pressure Problem

Click For Summary
SUMMARY

The pressure inside a vertical cylinder fitted with a frictionless piston can be calculated by considering both the weight of the piston and the atmospheric pressure. In this case, with a piston mass of 13 kg and a cross-sectional area of 0.04 m², the force exerted by the piston is 127.4 N (13 kg * 9.8 m/s²). The pressure exerted by the piston alone is 3185 Pa, but the total pressure must also include atmospheric pressure (101325 Pa), resulting in a final pressure of 104510 Pa (3185 Pa + 101325 Pa). This adjustment is necessary to account for the external atmospheric pressure acting on the piston.

PREREQUISITES
  • Understanding of basic physics concepts such as force, pressure, and equilibrium.
  • Familiarity with the ideal gas law and its application in pressure calculations.
  • Knowledge of units of pressure, specifically Pascal (Pa) and atmosphere (atm).
  • Ability to perform calculations involving mass, gravity, and area.
NEXT STEPS
  • Study the ideal gas law and its implications for pressure and volume changes.
  • Learn about the concept of atmospheric pressure and its effects on closed systems.
  • Explore the principles of hydrostatics and how they relate to gas pressure in cylinders.
  • Investigate real-world applications of pressure calculations in engineering and physics.
USEFUL FOR

Students in physics or engineering, professionals working with gas systems, and anyone interested in understanding pressure dynamics in closed environments.

lawgurl
Messages
2
Reaction score
0
Here is my problem.

A vertical cylinder of cross-sectional area .04m^2 if fitted with a frictionless piston with a mass of 13kg. Assume acceleration of gravity is 9.8 m/s^2. If there is 1 mol of an ideal gas in the cylinder at 315 K, find the pressure in the cylinder. Assume the system is in equilibrium.

Here is what I've been doing.

P=Force/Area Force= Pressue * Area

Since it is in equilibrium, the downward force of the piston should equal the upward force of the gas.

PA = (Piston mass)(gravity)

P(.04) = (13)(9.8)
P = 3185 Pa

3185 is not the right answer according to my online answer checker. What am I doing wrong?
 
Physics news on Phys.org
Questionable Solution

Okay, I found why my answer is wrong. Apparently I need to at 101300 Pa (1 atm) to my answer. If anyone can explain why I add one atmosphere, that would be greatly appreciated.
 
Assume the piston seals the vertical cylinder. The piston has a mass (13 kg) but also, there is atomspheric pressure outside the cylinder, i.e. the air in which we live, and that pressure is 1 atm = 14.7 psia = 101325 Pa or 101.325 kPa. At equilibrium, the pressure inside the cylinder must equal the pressure applied from the outside which is the sum of the (weight of the piston)/(area of piston), or (13 kg)(9.8 m/s2)/(0.04 m2) + the atmospheric pressure 101325 Pa.

mg = force = N if m (kg) and g (m/s2).

Pressure = force/area = N/m2 = Pa.
 
Last edited:

Similar threads

Adiabatic Expansion of Pressurized Air in a Piston-Cylinder Setup
  • · Replies 8 ·
Replies
8
Views
2K
Atmospheric Pressure on Shaft of piston cylinder assembly
  • · Replies 3 ·
Replies
3
Views
5K
What is the relationship between tire size and pressure changes?
  • · Replies 13 ·
Replies
13
Views
1K
Pressure-Volume Work
  • · Replies 7 ·
Replies
7
Views
1K
Ideal gas in a cylinder with a piston
  • · Replies 5 ·
Replies
5
Views
11K
Thermal energy problem: Gas expansion in cylinder
  • · Replies 3 ·
Replies
3
Views
3K
Understanding Pascal's Law: Why is Force Greater in One Cylinder Than the Other?
  • · Replies 1 ·
Replies
1
Views
2K
Thermodynamics- Piston problem, pressure, internal energy
  • · Replies 5 ·
Replies
5
Views
2K
Stationary vertical cylinder with heavy piston
  • · Replies 3 ·
Replies
3
Views
3K
First Law of Thermodynamics - Piston
  • · Replies 19 ·
Replies
19
Views
2K