Question

A gas is contained in a vertical, frictionless piston–cylinder device. The piston has a mass of 3.2 kg and a cross-sectional area of 35 cm2. A compressed spring above the piston exerts a force of 110 N on the piston. If the atmospheric pressure is 95 kPa, determine the pressure inside the cylinder.

Answer 1

To determine the pressure inside the cylinder, we need to consider the forces acting on the piston. The force exerted by the compressed spring is 110 N, and the weight of the piston can be calculated as the product of its mass (3.2 kg) and the acceleration due to gravity (9.8 m/s²). Substituting the given values, the pressure inside the cylinder is calculated to be 33714.29 Pa.

Step-by-step explanation:

To determine the pressure inside the cylinder, we need to consider the forces acting on the piston. The force exerted by the compressed spring is 110 N, and the weight of the piston can be calculated as the product of its mass (3.2 kg) and the acceleration due to gravity (9.8 m/s²). Since the piston is in equilibrium, the sum of these forces equals the pressure exerted by the gas inside the cylinder multiplied by the cross-sectional area of the piston.

Using the equation:

Force by spring + Weight of piston = Pressure inside cylinder x Area of piston

We can rearrange it to solve for the pressure inside the cylinder:

Pressure inside cylinder = (Force by spring + Weight of piston) / Area of piston

Substituting the given values, we have:

Pressure inside cylinder = (110 N + 3.2 kg * 9.8 m/s²) / 35 cm²

Converting the area to square meters:

Area of piston = 35 cm² * (1 m / 100 cm) * (1 m / 100 cm) = 0.0035 m²

Now we can calculate the pressure inside the cylinder:

Pressure inside cylinder = (110 N + 3.2 kg * 9.8 m/s²) / 0.0035 m²

Finally, we can solve for the pressure inside the cylinder using the given values:

Pressure inside cylinder = (110 N + 3.2 kg * 9.8 m/s²) / 0.0035 m² = 33714.29 Pa

Answer 2

146.826 KPa

Step-by-step explanation:

Given:

The mass of the piston = 3.2 kg

Cross-sectional area = 35 cm²

Force exerted by the spring = 110 N

Atmospheric pressure = 95 KPa

Now,

the total pressure inside the cylinder is the sum of all the pressure exerted on it i,e the pressure due the weight of the piston, pressure due to the force by the spring and the atmospheric pressure.

Now,

the pressure due to the weight of the piston = Weight / Area

= 3.2× 9.81 / 0.0035

= 31.392 / 0.0035

= 8969 Pa

= 8.969 KPa

And,

The pressure by the spring = 150 N / 0.0035

or

The pressure by the spring = 42,857 Pa = 42.857 KPa

Thus,

The total pressure

95 + 8.969 + 42.857 = 146.826 KPa