Question

$800\,cc$ volume of a gas having $\gamma =\frac{5}{3}$ is suddenly compressed adiabatically to $100\,cc$ . If the initial pressure is P, then the final pressure will

• A. $\frac{p}{32}$
• B. $\left( \frac{24}{5} \right)p$
• C. $8P$
• D. $\text{32 }P$

Answer 1

Answer: (D)

$\text{32 }P$

Answer 2

$P{{V}^{\gamma }}=constant$
$\Rightarrow$ $\frac{{{p}_{2}}}{{{p}_{1}}}={{\left( \frac{{{V}_{1}}}{{{V}_{2}}} \right)}^{\gamma }}$
$\therefore$ $\frac{{{p}_{2}}}{p}={{\left( \frac{800}{100} \right)}^{5/3}}$
$\Rightarrow$ ${{p}_{2}}=32p$