Question

$400cc$ volume of a gas having $\gamma =\frac{5}{2}$ is suddenly compressed to $100cc$ 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 ${\text{P}}_2{\text{V}}_2^{\gamma }={\text{P}}_1{\text{V}}_1^{\gamma }$
$\text{or}{\left(\text{P}\right)}_2={\left(\text{P}\right)}_1{\left(\frac{{\left(\text{V}\right)}_1}{{\left(\text{V}\right)}_2}\right)}^{\gamma }=\text{P}{\left(\frac{\text{400}}{\text{100}}\right)}^{5/2}=\text{P}\times 4\times 4\sqrt{4}=32\text{P}$