How Is Gauge Pressure Calculated in a Piston-Cylinder System?

Sarah were discussing the calculation of the gauge pressure of a piston-cylinder system. Chetan mentioned that the piston's radius, mass, and the applied force were given, and shared a picture of the system. Sarah then mentioned the relevant equations for calculating pressure and force, and also brought up the possibility of accounting for the piston's mass. In summary, the gauge pressure of the system can be found by dividing the applied force by the area of the piston. If the piston's mass is ignored, the pressure is 9.54 kPa, but if it is taken into account, the pressure is 13.3 kPa.
  • #1
raddian
66
0

Homework Statement


Find the gauge pressure of a piston-cylinder system, assuming that the piston perfectly covers the cylinder. The piston's radius is 5 cm, its mass is 3kg, and the force being applied to it is 75N in the same direction as gravity. Looks like this picture: http://www.ohio.edu/mechanical/thermo/Intro/Chapt.1_6/energy_eqns/energy_eqn.gif
and the force is downwards on the pistom.

Homework Equations


P=F/A
F=ma

The Attempt at a Solution


The answer depends on whether or not the mass should be taken into account.

Ignoring piston's mass:
P= 75N/(π(5cm/100)^2)=9.54e3 Pa = 9.54 kPa

Accounting for piston's mass:
P =((ma)+75N/(π(5cm/100)^2)) = ([(3kg)(9.81m/s/s]+75N)/(π(5cm/100)^2) = 13.3e3 Pa = 13.3 kPA
 
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  • #2
So what's the force per unit area being exerted on the gas in the cylinder (at the lower face of the piston)?

Chet
 

Related to How Is Gauge Pressure Calculated in a Piston-Cylinder System?

1. What is the formula for calculating pressure?

The formula for calculating pressure is P = F/A, where P is the pressure, F is the force, and A is the area.

2. How do I find the force on a piston?

The force on a piston can be found by multiplying the pressure by the area of the piston. The formula is F = P x A.

3. What units are used to measure pressure?

Pressure can be measured in various units, including Pascals (Pa), atmospheres (atm), pounds per square inch (psi), and millimeters of mercury (mmHg). It is important to use the correct units when calculating pressure.

4. How does the size of the piston affect the pressure?

The size of the piston indirectly affects the pressure by changing the area in the formula. A larger piston will have a larger area, resulting in a lower pressure for the same force. Conversely, a smaller piston will have a smaller area, resulting in a higher pressure for the same force.

5. Can pressure be negative?

Pressure is a scalar quantity and can be positive or negative. Negative pressure typically indicates a decrease in pressure, while positive pressure indicates an increase. However, negative pressure can also occur in certain situations, such as in a vacuum or when a force is pulling instead of pushing.

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