Question

$400 \, cc$ volume of a gas having $\gamma =\frac{5}{2}$ is suddenly compressed to $100 \, cc$ through an adiabatic process. If the initial pressure is $P$ , then the final pressure will be

• A. $P/32$
• B. $8P$
• C. $32 \text{P}$
• D. $16P$

Answer 1

Answer: (C)

Here $\text{V}_{1} = \text{400} \text{cc} \text{,} \text{V}_{2} = \text{100} \text{cc} \text{ ;} \gamma = \frac{5}{2}$
Sudden compression is an adiabatic process.
For an adiabatic process, $\text{PV}^{\gamma } = \text{constant}$
As $\text{P}_{2} \text{V}_{2}^{\gamma } = \text{P}_{1} \text{V}_{1}^{\gamma }$
$\text{or} \left(\text{P}\right)_{2} = \left(\text{P}\right)_{1} \left(\frac{\left(\text{V}\right)_{1}}{\left(\text{V}\right)_{2}}\right)^{\gamma } = \text{P} \left(\frac{\text{400}}{\text{100}}\right)^{5 / 2} = \text{P} \times 4 \times 4 \sqrt{4} = 3 2 \text{P}$