A vertical closed cylinder is separated into two parts by a frictionless piston of…

PHYSICS · Single correct · AP · Physics 2: Algebra-based · Thermodynamics · Thermodynamics

Problem

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 the 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) (1)

\frac{RT}{ng} \left[ \frac{l_1 - 3l_2}{l_1 l_2} \right]

(2)

\frac{RT}{g} \left[ \frac{2l_1 + l_2}{l_1 l_2} \right]

(3)

\frac{nRT}{g} \left[ \frac{1}{l_2} + \frac{1}{l_1} \right]

(4)

\frac{nRT}{g} \left[ \frac{l_1 - l_2}{l_1 l_2} \right]