Question

The cylinder in FIGURE Q18.4 is divided into two compartments by a frictionless piston that can slide back and forth. If the piston is in equilibrium, is the pressure on the left side greater than, less than, or equal to the pressure on the right? Explain.

FIGURE Q18.4

Short answer

As Force $\left(F\right)$and Cross Sectional Area $\left(A\right)$is same on either sides of the Piston, thus the pressure is same on Both Sides of the Piston from the two compartments.

Step-by-step solution

Concept

An amount of force that is applied on a per unit area is known as Pressure. Under the circumstances of Equilibrium Condition, the amount of Net Force that is present on the Piston that is acting as a barrier between the two compartments is zero.

The Formula of Pressure is:

$P=\frac{F}{A}$

where,$F$is Force and$A$is cross sectional Area.

Explanation related to Pressure applied on the Piston

As per the laws of Equilibrium, in case the frictionless Piston is in Equilibrium Condition, the net force that is present on the Piston is equal to Zero. This means that the amount of pressure that is being enforced on the Piston from the Left Side Compartment is equal in magnitude to the amount of pressure that is being enforced on the Piston from the Right Side Compartment. From the provided image in the question ( FIGURE Q18.4 ),it is clear that the cross sectional area of the Piston is equal on both the sides that it is sharing with the two compartments. Thus, it can be concluded that, Force $\left(F\right)$and Cross Sectional Area $\left(A\right)$is equal on both sides of the Piston and so pressure is same on the left and right side of the Piston.