MHT CET · Physics · Thermodynamics
A polyatomic gas \(\left(Y=\frac{4}{3}\right)\) is compressed to \(\left(\frac{1}{8}\right)^{\text {th }}\) of its volume adiabatically. If its initial pressure is \(p\), its new pressure will be
- A 8p
- B 16p
- C 2p
- D 6p
Answer & Solution
Correct Answer
(B) 16p
Step-by-step Solution
Detailed explanation
For an adiabatic process: \(p V \gamma=\) constant
Let initial pressure be \(p\) and volume \(V\), then the final pressure is \(P\)
and volume \(\frac{V}{8}\).
\(\begin{aligned}
& \Rightarrow p V^{4 / 3}=P\left(\frac{V}{8}\right)^{4 / 3} \\
& \Rightarrow P=8^{4 / 3} p=16 p
\end{aligned}\)
Let initial pressure be \(p\) and volume \(V\), then the final pressure is \(P\)
and volume \(\frac{V}{8}\).
\(\begin{aligned}
& \Rightarrow p V^{4 / 3}=P\left(\frac{V}{8}\right)^{4 / 3} \\
& \Rightarrow P=8^{4 / 3} p=16 p
\end{aligned}\)
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