Question

A gas of unknown pressure is contained in a vertical cylinder with a piston, of mass 1.1 kg and diameter 10.0 cm. The piston is free to move with negligible friction. A weight of mass 2.0 kg is placed on top of the piston. Knowing the atmospheric pressure (1.0 atm), find the pressure of the gas, in pascals.

Answer 1

Answer:

The answer the question, what is the pressure of the gas, in pascals is 101195.73 Pa

Explanation:

Firstly we list out the known variables

The known variables are

mass of piston = 1.1 kg, diameter of piston, D = 10.0 cm = 0.1 m

mass of weight = 2.0 kg atmospheric pressure = 1.0 atm

In this question the quantity required is the presssure of the gas in the cylinder after placing a weght on the piston

To solve this, we note that Pressure = Force per unit area

= Force/area, hence

We compute the area of the piston thus

Area = (πD²)÷4 = 0.0079 m²

While the sum of the mass of the piston and the added weight = 1.1 kg + 2.0 kg = 3.1 kg

The weight of the added mass and piston that is their force on the gas = W = Mass × gravity = 3.1 kg × 9.81 m/s² = 30.411 N

Therefore the pressure  = 30.411N/(0.0079 m²) = 3870.73 Pascals

The pressure of the gas = pressure due to the piston and the added weight + pressure due to the atmosphere

thus pressure of the gas = 3870.73 Pa + 1.0 atm =3870.73 Pa + 101325 Pa =101195.73 Pa

The pressure of the gas, in pascals is 101195.73 Pa