Pressure on a piston in a cylinder

Click For Summary
SUMMARY

The pressure inside a vertical cylinder with a frictionless piston, given a cross-sectional area of 0.25 m², a piston mass of 22 kg, and an ideal gas at 310 K, is calculated using the formula Pressure = F/Area. The force is derived from the weight of the piston (22 kg x 9.8 m/s²), resulting in a pressure of 1.02 x 10⁵ Pa when atmospheric pressure is included. The volume of the gas is determined using the ideal gas law PV = nRT, yielding a volume of 0.025 m³, which corresponds to a piston height of 0.1 m or 10 cm.

PREREQUISITES
  • Understanding of basic physics concepts such as pressure and force.
  • Familiarity with the ideal gas law (PV = nRT).
  • Knowledge of unit conversions, particularly between pressure units and metric measurements.
  • Ability to perform calculations involving area and volume in a cylindrical context.
NEXT STEPS
  • Review the ideal gas law and its applications in thermodynamics.
  • Study the relationship between pressure, volume, and temperature in gas systems.
  • Learn about the effects of atmospheric pressure on gas calculations.
  • Explore advanced topics in fluid mechanics related to piston-cylinder systems.
USEFUL FOR

Students studying physics, particularly those focusing on thermodynamics and fluid mechanics, as well as educators seeking to clarify concepts related to pressure and gas laws.

Jimkatz809
Messages
7
Reaction score
0

Homework Statement



A vertical cylinder of cross-sectional area 0.25 m2 is fitted with a tight-fitting, frictionless piston of mass 22 kg. The acceleration of gravity is 9.8 m/s2 . If there are 1 mol of an ideal gas in the cylinder at 310 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


Pressure=F/Area
PV=nRT
Height= Volume /Area



The Attempt at a Solution


Pressure =F/Area (22kg x 9.8m/s^2)/(0.25m^2) Then I added atmospheric pressure to this pressure which is 1.013x10^5 Pa. I got an answer for pressure as 1.02x10^5 Pa and I got it correct.
Then for volume I have been trying V= (1 mol x 8.3145 x 310 K)/(1.02x10^5) and I get .025 as my volume but I think this number is off and I can't figure out why... I don't want to move forward until I figure this part out.
 
Physics news on Phys.org
.025 looks good to me.
 
The volume is correct, in m^3. The question asks for the height, which is .025/.25 = .1 m or 10 cm. What is the answer you are given?

AM
 
I the calculations as you said and got .1 m just as you said and I tried puting it into the UTexas system but its said that is wrong. I don't understand because it makes no sense that should be the answer.
 
Jimkatz809 said:
I the calculations as you said and got .1 m just as you said and I tried puting it into the UTexas system but its said that is wrong. I don't understand because it makes no sense that should be the answer.
Try .10 m (two sig. figures).

AM
 

Similar threads

Adiabatic Expansion of Pressurized Air in a Piston-Cylinder Setup
  • · Replies 8 ·
Replies
8
Views
2K
Extension of spring in a system with two pistons
  • · Replies 16 ·
Replies
16
Views
909
What is the relationship between tire size and pressure changes?
  • · Replies 13 ·
Replies
13
Views
1K
Calculation of Tensile Forces in Piston-Type Water-Lifting Devices at Elevated Locations
  • · Replies 15 ·
Replies
15
Views
717
Thermal energy problem: Gas expansion in cylinder
  • · Replies 3 ·
Replies
3
Views
3K
Proof question related to the Ideal Gas Law
  • · Replies 8 ·
Replies
8
Views
2K
Pressure of a piston cylinder device after heated
  • · Replies 3 ·
Replies
3
Views
3K
Atmospheric Pressure on Shaft of piston cylinder assembly
  • · Replies 3 ·
Replies
3
Views
5K
Ratio of volumes in a vertical cylinder with a piston
  • · Replies 3 ·
Replies
3
Views
880
First Law of Thermodynamics - Piston
  • · Replies 19 ·
Replies
19
Views
2K