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.

Question

Philoid · Accepted Answer

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