Suppose a monatomic ideal gas is contained within a vertical cylinder that is fitted with a movable piston. The piston is frictionless and has a negligible mass. The area of the piston is 3.06 10-2 m2, and the pressure outside the cylinder is 1.02 105 Pa. Heat (2109 J) is removed from the gas. Through what distance does the piston drop?
To determine the distance the piston drops, we can use the equation for work done on a gas:
Work = Force x Distance
In this case, the work done on the gas is equal to the heat removed from the gas. The force exerted on the piston is the pressure outside the cylinder multiplied by the area of the piston.
First, let's calculate the force exerted on the piston:
Force = Pressure x Area
Force = 1.02 x 10^5 Pa x 3.06 x 10^-2 m^2
Next, we can rearrange the equation for work to solve for distance:
Distance = Work / Force
Distance = 2109 J / (1.02 x 10^5 Pa x 3.06 x 10^-2 m^2)
Now, let's calculate the distance:
Distance = 2109 J / (3.1122 N)
Distance ≈ 678.03 meters
Therefore, the piston will drop approximately 678.03 meters.