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Three samples A, B and C of the same gas  (γ=1.5) have equal volumes and temperatures. The volu me of each sample is doubled, the process being isother mal for A, adiabatic for B and isobaric for C. If the final pressures are equal for the three samples, Find the ratio of the initial pressures.


Solution

VA=VB=VC                    TA=TB=Tc

For  A the process is isothermal

PA VA=PA 2VA

PA=PA×12

For B the process is adiabatic

PBVγB=PB(2VB)

PB=PB21.5

For  C the process   is adiabatic

VCTC=VCTCVCTC=2VCTC

Tc=2TC

Final pressure are equal

PA2=PB21.5=PC

PA:PB:PC=2:21.5:1

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