The correct option is C 128
Given,
Initial state of gas (P,ρ)
Final state of gas (P′,ρ′)
We know that, mass density (ρ)∝1V
Thus, V1V2=ρ2ρ1 .....(1)
where V is the volume and ρ is mass density.
Assuming no of moles of diatomic gas is constant.
From the equation of state of gas during an adiabatic process
P2Vγ2=P1Vγ1
we get, P2P1=(V1V2)γ,
Using equation (1) and from the data given in the question,
P′P=(ρ2ρ1)γ=(ρ′ρ)γ=(32)75
⇒P′P=27=128
Thus, option (c) is the correct answer.