Suppose a monatomic ideal gas is contained within a
verticalcylinder that is fitted with a movable piston. the piston
isfrictionless and has a negligible mass. the area of thepiston is
3.14 x 10^ -2 m^2, and the pressure outside the cylinderis 1.01 x
10^5 pa. heat (2093 j) is removed from thegas. through what
distance does the piston drop?

From the conservation of energy law at steady state conditions given,

Heat removed from the gas Q, = Work done by the piston, W = PdV = PAdL

where

P = Pressure difference =  1.01 X 10^5 Pa

A=Piston area =3.14 X 10^ -2 m^2

dL = distance moved (dropped) by the piston ?

Q=2093J

2093 = 101000 x 0.0314 x dL

dL = 0.6590.66m

Therefore, the distance dropped by the piston = 0.66m

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