In an adiabatic process, the density of a diatomic gas becomes 32 n times its initial value. The final pressure of the gas is found to be n times the initial pressure. The value of n is:

Step-by-step solution

Given, Final density of diatomic gas is ρ f = 32 n ρ i Final pressure is P f = n P i In adiabatic process, equation of state is given by, P V γ = constant     . . . 1 Where, V is the volume, P is the pressure and γ = 7 5 is the ratio of specific heat of diatomic gas P m ρ γ = constant     . . . 2 , As V = m ρ and mass is constant, then the pressure is given by ∴ P ∝ ρ γ ⇒ P f P i = ρ f ρ i γ ⇒ n P i P i = 32 &#96