Three samples A, B and C of the same gas (γ = 1.5) have equal volumes and temperatures. The volume of each sample is doubled, the process being isothermal for A, adiabatic for B and isobaric for C. If the final pressure is equal for the three samples, find the ratio of the initial pressures.

Let VA, VB, VC be the volume of three gases and TA, TB, TCbe the temperature of A, B, C gas


Given, TA=TB=TC, VA=VB=VC


Here A is undergoing an isothermal process, where V1= VA, V2=2VA


Let P1 and P2 be the initial and final pressures,


Then,





Here B is adiabatic,


PVγ = const, where V1= VB, V2=2VB


Let P1 and P2 be the initial and final pressures,


I.e.




Here C is isobaric ,the pressure remains constant and equal to


Now, as the final pressures are equal for all the gases



, ratio of the initial pressures


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