An ideal mono-atomic gas is confined in a cylinder with the help of a piston that can slide inside the cylinder without friction. The cylinder is placed on a horizontal platform in a vacuum chamber. The walls of the cylinder and the piston are made of heat insulating materials. Initially the temperature of the gas is T0 and the piston stays in equilibrium as shown in the figure. The temperature of the gas is quickly increased η times and then the gas is allowed to expand. If the piston rises and again acquires an equilibrium state, find temperature of the gas in this new equilibrium state. (in kelvin) (Take, η=2, T0=273K )

Question

An ideal mono-atomic gas is confined in a cylinder with the help of a piston that can slide inside the cylinder without friction. The cylinder is placed on a horizontal platform in a vacuum chamber. The walls of the cylinder and the piston are made of heat insulating materials. Initially the temperature of the gas is T0   and the piston stays in equilibrium as shown in the figure. The temperature of the gas is quickly increased η   times and then the gas is allowed to expand. If the piston rises and again acquires an equilibrium state, find temperature of the gas in this new equilibrium state. (in kelvin) (Take, η=2,   T0=273K )

Accepted Answer

P0,V0,T0I→ηP0,V0,ηT0II→P0,Vf,TfIII P0=mgA  Wg=−Wext=P0ΔV=P0(Vf−V0)=nR(Tf−T0) Applying 1st law on gas for  II→III ΔQ°=ΔU+ΔW⇒O=32nR(Tf−ηT0)+nR(Tf−T0) ⇒Tf=(3η+25)T0=85×273=436.80

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