Two geometrically identical cylinders of inner diameter 5.0 cm, one made of copper and the...

SKETCH:

Two geometrically identical cylinders, one made up of copper and the other of Teflon, are immersed in a large-volume water tank at room temperature as shown in the figure below.

RESEARCH:

The Ideal Gas Law is given by

For the copper cylinder, the process is isothermal process. As the temperature remains constant in isothermal process, according to Ideal Gas Law we have

…… (1)

For the Teflon cylinder, the process is adiabatic, and for an adiabatic process

…… (2)

As the Helium is a monatomic gas, the ratio of molar specific heats is

SIMPLIFY:

(a) Initially at the equilibrium, the net force acting on the piston is zero, so by ’s second law:

…… (3)

After the lead block is placed on the platter, at the equilibrium, the net force acting on the piston is zero, so by ’s second law:

From the equation (1), the final height of the Copper piston is

…… (5)

From the equation (2), the final height of the Teflon piston is

…… (6)

CALCULATE:

(a) Substituting the given values in equation (3), the initial pressure is

Substituting the given values in equation (4), the final pressure is

Substituting the given values in equation (5), the final height of the Copper piston is

Substituting the given values in equation (6), the final height of the Teflon piston is

(b) If the blocks are dropped suddenly on their platters, the compression of helium in the copper cylinder will no longer be an isothermal process since there will be heat flow into the helium gas, and it is closer to an adiabatic change as the compression occurs more rapidly. Therefore, the final equilibrium heights will be the same as that calculated in part-(a).