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Q.

One mole of an ideal monoatomtic gas in an intial state a with pressure  Pi and volume  Vi is to be taken to a final state d with Pf=B2Pi  and  Vf=Vi/B  through the path  abcd  as shown in figure below for a particular value of  B(>1) . Here  ab  and  cd   are adiabatic paths while bc  is an isothermal  process with temperature  T0. States b and c correspond to  (P1,V1)  and  (P2,V2)  respectively.

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a

The ratio of  V2V1  is  B

b

The ratio of  V2V1  is  B3

c

Work done by the gas is  RT02lnB+32(RT0BPiVi)

d

Work done by the gas is RT02lnB+32PiVi(1B)

answer is A, C.

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Detailed Solution

 ab:piviγ=p1v1γ(i) cd:pfvfγ=p2v2γ(ii) bc:p1v1=p2v2(iii)
Dividing (2) by (1), we get
v2v1=B2γγ1=B[γ=53]
Work done by the gas
W=Wab+Wbc+Wcd=RT02lnB+32pivi(1B)

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