Pressure on a piston in a cylinder

In summary, a vertical cylinder with a cross-sectional area of 0.25 m2 and a tight-fitting, frictionless piston of mass 22 kg, containing 1 mol of an ideal gas at 310 K, will have a pressure of 1.02x10^5 Pa inside the cylinder. The piston will be in equilibrium under its own weight at a height of 10 cm or 0.10 m. The formula used for pressure is F/Area and the formula for volume is PV=nRT.
  • #1
Jimkatz809
8
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.
 
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  • #2
.025 looks good to me.
 
  • #3
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
 
  • #4
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.
 
  • #5
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
 

Related to Pressure on a piston in a cylinder

What is pressure on a piston in a cylinder?

Pressure on a piston in a cylinder refers to the force exerted by a gas or liquid on the surface of a piston inside a closed cylinder.

How is pressure on a piston in a cylinder measured?

Pressure on a piston in a cylinder is typically measured in units of pressure, such as pounds per square inch (psi) or kilopascals (kPa).

What factors affect pressure on a piston in a cylinder?

The pressure on a piston in a cylinder is affected by the amount of gas or liquid inside the cylinder, the size and shape of the piston, and the temperature of the gas or liquid.

What is the relationship between pressure on a piston in a cylinder and volume?

According to Boyle's law, when the temperature is constant, pressure and volume have an inverse relationship. This means that as pressure on a piston in a cylinder increases, volume decreases, and vice versa.

How is pressure on a piston in a cylinder used in real-world applications?

Pressure on a piston in a cylinder is used in many real-world applications, such as car engines, hydraulic systems, and scuba diving equipment. It is also important in understanding weather patterns and predicting changes in atmospheric pressure.

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