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MHT CET · Physics · Kinetic Theory of Gases

A gas at N.T.P. is suddenly compressed to \(\left(\frac{1}{4}\right)^{\mathrm{th}}\) of its original volume. The final pressure in (Given \(\gamma=\) ratio of sp. heats \(=\frac{3}{2}\) ) atmosphere is ( \(\mathrm{P}=\) original pressure \()\)

  1. A \(4\ P\)
  2. B \(\frac {3}{2}\ P\)
  3. C \(8\ P\)
  4. D \(\frac {1}{4}\ P\)
Verified Solution

Answer & Solution

Correct Answer

(C) \(8\ P\)

Step-by-step Solution

Detailed explanation

In Adiabatic compression, \(\mathrm{PV}^\psi=\) constant
Given \(\mathrm{V}_{\text {new }}=\frac{1}{4} \mathrm{~V}\) and \(\gamma=\frac{3}{2}\)
\(\begin{aligned}
& \therefore \quad \frac{\mathrm{P}_{\mathrm{new}}}{\mathrm{P}}=\left(\frac{\mathrm{V}}{\mathrm{V}_{\text {new }}}\right)^7=\left(\frac{\mathrm{V}}{\frac{1}{4} \mathrm{~V}}\right)^{3 / 2} \\
& \therefore \quad \mathrm{P}_{\mathrm{new}}=8 \mathrm{P}
\end{aligned}\)
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