Question

A polyatomic gas is compressed to \(\left(\frac{1}{8}\right)^{\text {th }}\) of its volume adiabatically. If its initial pressure is \(\mathrm{P}_0\), its new pressure will be [Given, \(\frac{\mathrm{C}_{\mathrm{p}}}{\mathrm{C}_{\mathrm{v}}}=\frac{4}{3}\) ]

• A. \(6\mathrm{P}_{0}\)
• B. \(2\mathrm{P}_{0}\)
• C. \(8\mathrm{P}_{0}\)
• D. \(16\mathrm{P}_{0}\)

Hint:

Use P V to the power gamma equal to a constant with gamma = 4/3.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept
For an adiabatic process \(P_0V_0^{\gamma}=P V^{\gamma}\).

Step 2: Substitute
\(V=\dfrac{V_0}{8}\) and \(\gamma=\dfrac43\), so \(P=P_0\left(\dfrac{V_0}{V}\right)^{4/3}=P_0\,8^{4/3}\).

Step 3: Calculation
\(8^{4/3}=(2^3)^{4/3}=2^4=16\), so \(P=16P_0\).

Final Answer:
The new pressure is 16 P0. \[ \boxed{\text{(D) }16\mathrm{P}_{0}} \]