20 points

A steel cylinder filled with a gas obeying the ideal gas law is covered on the top using an airtight

sealed cover plate. The cover plate is relatively light hence, for our analysis we will neglect any

weight of the plate. The cylinder has a circular cross-section of diameter D, and the coverplate is

originally at a height H. We are going to conduct an experiment where we will add small cubical

metal blocks of steel weighing w each, on top of the cover plate. After each weight added, we will

observe how much the cover plate slides down by and measure the height of the gas-filled container.

Assume that the gas was sealed originally at atmospheric pressure, and that the temperature of

the system does not change.

Problem 4

Part a: Draw a sketch to visually represent what this experiment will look like. You can sketch

the system at the initial time and at a time t when N(t) number of weights have been added on

the cover plate.

Part b: Identify the gas pressure that is needed to balance N(t) such weights.

Part c: Derive an expression that estimates the number of weights needed to reduce the gas volume

by a factor of a