Q. 6

An ideal gas is taken from an initial state i to a final state f in such a way that the ratio of the pressure to the absolute temperature remains constant. What will be the work done by gas?

Answer :

Given


Initial pressure Pi


Final pressure Pf


Initial temperature Ti


Final temperature Tf


It is given that



From ideal gas equation, we know


PV=nRT


Where V=volume of gas


R=gas constant


n= number of moles


applying ideal gas equation for both processes, we get



And



From equation (i), (ii) and (iii), we get



Vi=Vf


We know that,


Work done = force ×displacement



Volume = area ×displacement


Therefore,


Work done=pressure × volume


Let change in the volume of system = ΔV = Vf-Vi


Pressure =P


Thus, work done by the gas


ΔW=PΔV=P (Vf-Vi) =0


work done by the gas is zero.


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