A gas is contained in a vertical, friction less piston...

A gas is contained in a vertical, friction less piston cylinder device. The piston has a mass of $3.2 \mathrm{kg}$ and a cross sectional area of $35 \mathrm{cm}^{2}$. A compressed spring above the piston exerts a force of $150 \mathrm{N}$ on the piston. If the atmospheric pressure is $95 \mathrm{kPa}$, determine the pressure inside the cylinder.

Key Concepts

Spring Force

The force provided by a compressed or extended spring is determined by the spring's characteristics. In piston systems, an additional force from a spring must be taken into account when establishing the overall force balance and determining the internal pressure required to maintain equilibrium.

Atmospheric Pressure

Atmospheric pressure is the pressure exerted by the weight of the atmosphere. In the context of a piston-cylinder device, it acts as an external pressure on the piston, contributing to the force balance required for mechanical equilibrium in the system.

Force Balance in a Piston System

A piston system reaches equilibrium when the forces acting on the piston, from both the gas within and the external environment, cancel each other out. This involves accounting for the pressure force from the gas, the gravitational force from the piston’s mass, atmospheric pressure, and any additional external forces, thereby ensuring the piston remains stationary.

Mechanical Equilibrium

Mechanical equilibrium in a system means that all forces acting on the system are balanced, resulting in no net acceleration. In a piston-cylinder device, the forces from the gas pressure inside must balance against external forces such as atmospheric pressure, the weight of the piston, and any additional forces like those from a spring.

Pressure

Pressure is defined as the force exerted per unit area, and it is a fundamental concept in fluid mechanics and thermodynamics. In systems involving gases, pressure quantifies how the molecules of the gas push against the surfaces enclosing it.

Please give Ace some feedback