Question

A gas having \(\gamma=\frac{5}{2}\) and volume 360 c.c. is suddenly compressed to 90 c.c. If the initial pressure of the gas is P , then the final pressure will be

• A. \(\frac{\mathrm{P}}{4}\)
• B. 8 P
• C. 16 P
• D. 32 P

Hint:

Sudden changes in volume are always considered adiabatic.

Answer 1

The Correct Option is D

Step 1: Adiabatic Process
"Suddenly compressed" implies an adiabatic process where $PV^\gamma = \text{constant}$.

Step 2: Ratio Calculation
$P_1 V_1^\gamma = P_2 V_2^\gamma \implies P_2 = P \left( \frac{360}{90} \right)^{5/2}$. $P_2 = P (4)^{5/2}$.

Step 3: Calculation
$4^{5/2} = (\sqrt{4})^5 = 2^5 = 32$. $P_2 = 32 P$.
Final Answer: (D)