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: Write the ratio
$\dfrac{P}{P_0}=\left(\dfrac{V_0}{V}\right)^{\gamma}=8^{4/3}$.

Step 2: Simplify
$8^{1/3}=2$, so $8^{4/3}=2^4=16$.

Step 3: Result
$P=16P_0$.

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