First slide

Different type of processes

Question

The pressure and density of a diatomic gas $(γ = 7 / 5)$ change adiabatically from $(P, ρ) to (P', ρ') .$ If $(P' / P) = 32, (ρ' / ρ)$ should equal:

Easy

A

1/128
B

32
C

128
D

none of these

Solution

${Pρ}^{- γ} = constant \Rightarrow ρ^{1} = ρ {(\frac{P'}{P})}^{γ} = ρ {(32)}^{\frac{7}{5}} = ρ {(2)}^{7} = 128 \Rightarrow \frac{ρ'}{ρ} = 128 .$

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