Consider a tall vertical cylindrical container of height \"H\" at atmospheric pr

Question

Consider a tall vertical cylindrical container of height "H" at atmospheric pressure. A precisely fitted plug is dropped into the cylinder and falls - compressing the air. After a brief period of oscillation the plug settles to a height "h =H/2." Assume the air behaves as an ideal gas and this takes place at 27degree C. We now raise the temperature of the cylinder very slowly, causing the air to expand re-raising the piston. What is the temperature just before the piston reaches the top of the cylinder?

Explanation / Answer

Let volume of cylinder be V

when the plug is dropped, it settles to a height equal to half the height of the cylinder.

So new volume = V/2

The cylinder is initially at atmospheric pressure or 1 atm

Since the volume is halved, at constant temperature, the pressure inside doubles i.e. = 2 atm

Now we begin to heat the cylinder and the pressure inside is maintained constant.

Initial temperature T1 = 27 C = 300 K

Initial volume = V/2

Final volume = V (volume when the piston reaches the top of the cylinder)

V1/ T1 = V2 / T2

(V/2) / 300 K = V / T2

T2 = 600 K, So the temperature would be 600 K

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