A vertical closed cylinder is separated into two parts by a frictionless piston of mass m and of negligible thickness. The piston is free to move along the length of the cylinder. The length of the cy

Question

A vertical closed cylinder is separated into two parts by a frictionless piston of mass $m$ and of negligible thickness. The piston is free to move along the length of the cylinder. The length of the cylinder above piston is $l_{1},$ and that below the piston is $l_{2},$ such that $l_{1} > l_{2} .$ Each part of the cylinder contains $n$ moles of an ideal gas at equal temperature $T .$ If the piston is stationary, its mass $m$ will be given by:

( $R$ is universal gas constant and $g$ is the acceleration due to gravity)

Options:

Answer:

B

Solution:

$P_{1} + \frac{m g}{A} = P_{2}$

$\Rightarrow \frac{n R T}{l_{1} A} + \frac{m g}{A} = \frac{n R T}{l_{2} A}$

$\Rightarrow m = \frac{n R T}{g} (\frac{1}{l_{2}} - \frac{1}{l_{1}})$

$= \frac{n R T}{g} (\frac{l_{1} - l_{2}}{l_{1} l_{2}})$

TestHub · Accepted Answer

P 1 + m g A = P 2 ⇒ n R T l 1 A + m g A = n R T l 2 A ⇒ m = n R T g 1 l 2 - 1 l 1 = n R T g l 1 - l 2 l 1 l 2

Physics - Heat & Thermo Question with Solution | TestHub

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