A vertical cylinder of cross-sectional area `0.1m^(2)` closed at both ends is fitted with a frictionless piston of mass M dividing the cylinder into two parts. Each part contains one mole of an ideal gas in equilibrium at `300K`. The volume of the upper part is `0.1m^(3)` and that of lower part is `0.05m^(3)` .What force must be applied to the piston so that the volumes of the two parts remain unchanged when the temperature is increased to `500K`?

Answer

`1660N`

Explanation

`P_(1)A + Mg = P_(2)A`
Extra force needed
=`P'_(2)A - P'_(1)A -Mg`
=`P'_(2)A - P'_(1)A - P_(2)A + P_(1)A`
= `(DeltaP_(2)) A - (DeltaP_(1))A`
=`[(nRDeltaT)/(V) - (nRDeltaT)/(2V)]A = (5000)/(3)N`