Question:hard
The pressure \(P_1\) and density \(d_1\) of a diatomic gas change to \(P_2\) and \(d_2\) during an adiabatic operation. Find the value of
\[
\frac{P_1}{P_2},
\]
if
\[
\frac{d_2}{d_1}=32.
\]
The pressure \(P_1\) and density \(d_1\) of a diatomic gas change to \(P_2\) and \(d_2\) during an adiabatic operation. Find the value of
\[
\frac{P_1}{P_2},
\]
if
\[
\frac{d_2}{d_1}=32.
\]
Show Hint
For adiabatic processes,
\[
P\propto d^\gamma.
\]
Remember:
\[
\gamma=\frac53 \text{ (monoatomic)},
\qquad
\gamma=\frac75 \text{ (diatomic)}.
\]
Convert the density ratio directly into a pressure ratio using this relation.
Updated On: Jul 29, 2026
- \(128\)
- \[ \frac{1}{64} \]
- \(64\)
- \[ \frac{1}{128} \]
Show Solution
The Correct Option is D
Solution and Explanation
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