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 V_{A}, VB, VC be the volume of three gases and T_{A}, TB, TCbe the temperature of A, B, C gas

Given, T_{A}=T_{B}=T_{C}, V_{A}=V_{B}=V_{C}

Here A is undergoing an isothermal process, where V1= V_{A}, V2=2V_{A}

Let P1 and P2 be the initial and final pressures,

Then,

Here B is adiabatic,

PV^{γ} = const, where V1= V_{B}, V2=2V_{B}

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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