JEE Challenger
More from Thermodynamics
PhyHardAdv 2007 • Paper 1

Pressure in Cylinder When Piston is Pulled Slowly

The piston is now pulled out slowly and held at a distance 2L2L from the top. The pressure in the cylinder between its top and the piston will then be

Options

A

P0P_0

Correct
B

P02\frac{P_0}{2}

C

P02+MgπR2\frac{P_0}{2} + \frac{M g}{\pi R^2}

D

P02−MgπR2\frac{P_0}{2} - \frac{M g}{\pi R^2}

Topics & Concepts

ThermodynamicsFirst Law of ThermodynamicsKinetic Theory of Gases

Step-by-Step Solution

Based on the context of the problem, the cylindrical vessel is vertically oriented with an open hole at the top.

  1. State of the Hole at the Top:
    Initially, the hole at the top of the cylinder is not sealed (as indicated by the subsequent question, where it is explicitly stated: "While the piston is at a distance 2L2L from the top, the hole at the top is sealed").

  2. Pressure Inside the Cylinder:
    Since the hole at the top remains open to the atmosphere during the process of pulling out the piston slowly, air freely enters the cylinder from the outside.

  3. Conclusion:
    As a result of continuous communication with the atmosphere through the open hole, the pressure of the air inside the cylinder between its top and the piston remains equal to the atmospheric pressure, P0P_0.

Therefore, the pressure in the cylinder between its top and the piston is P0P_0.

Correct Option: (A)

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