MHT CET · Physics · Thermodynamics
A gas at N.T.P. is suddenly compressed to onefourth of its original volume. If \(\gamma=1.5\), then the final pressure is
- A 4 times
- B 1.5 times
- C 8 times
- D \(\frac{1}{4}\) times
Answer & Solution
Correct Answer
(C) 8 times
Step-by-step Solution
Detailed explanation
As the change is sudden, the process is adiabatic
\(\begin{array}{ll}
\therefore & \mathrm{P}_1 \mathrm{~V}_1^\gamma=\mathrm{P}_2 \mathrm{~V}_2^\gamma \\
\therefore & \frac{\mathrm{P}_2}{\mathrm{P}_1}=\left[\frac{\mathrm{V}_1}{\mathrm{~V}_2}\right]^\gamma=\left[\frac{4}{1}\right]^{3 / 2}=\frac{8}{1}
\end{array}\)
\(\begin{array}{ll}
\therefore & \mathrm{P}_1 \mathrm{~V}_1^\gamma=\mathrm{P}_2 \mathrm{~V}_2^\gamma \\
\therefore & \frac{\mathrm{P}_2}{\mathrm{P}_1}=\left[\frac{\mathrm{V}_1}{\mathrm{~V}_2}\right]^\gamma=\left[\frac{4}{1}\right]^{3 / 2}=\frac{8}{1}
\end{array}\)
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