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Question

The pressure and density of a diatomic gas (γ=75) changes from (P,ρ) to (P,ρ) during an adiabatic change. If ρρ=32, then the value of PP is
  1. 36
  2. 1128
  3. 128
  4. 136


Solution

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,
PP=(ρ2ρ1)γ=(ρρ)γ=(32)75
PP=27=128
Thus, option (c) is the correct answer.

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