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 :


Initial pressure Pi

Final pressure Pf

Initial temperature Ti

Final temperature Tf

It is given that

From ideal gas equation, we know


Where V=volume of gas

R=gas constant

n= number of moles

applying ideal gas equation for both processes, we get


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


We know that,

Work done = force ×displacement

Volume = area ×displacement


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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