Q138 / 160 · TS EAMCET 2004 · Physics

The pressure and density of a given mass of a diatomic gas $\left(\gamma=\frac{7}{5}\right)$ change adiabatically from $(P, d)$ to $\left(P^{\prime}, d^{\prime}\right)$. If $\frac{d^{\prime}}{d}=32$, then $\frac{P^{\prime}}{P}$ is ( $\gamma=$ ratio of specific heats $)$

  • A
    $\frac{1}{128}$
  • B
    $\frac{1}{64}$
  • C
    $64$
  • Correct answer
    D
    $128$

Solution

$\begin{aligned} & p V^\gamma=\frac{p}{\rho^\gamma}=\text { constant } \\ & \therefore \quad \frac{p^{\prime}}{p}=\left(\frac{\rho^{\prime}}{\rho}\right)=(32)^{7 / 5} \\ & =32 \times 4=128 \\ & \end{aligned}$

Hence, the correct answer is option: 'D'.

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