Q. A gas at pressure $p$ is adiabatically compressed so that its density becomes twice that of initial value. Given that $\gamma = C_{p}/C_{v} = 7/5$, what will be the final pressure of the gas?
A) $2\ p$
B) $\frac{7}{5}p$
C) $2.63\ p$
D) $p$
Explanation
(c) As $p_{2}V_{2}^{\gamma} = p_{1}V_{1}^{\gamma}$
$\therefore\ \ p_{2} = p_{1}\left( \frac{V_{1}}{V_{2}} \right)^{\gamma} = p_{1}\left( \frac{\rho_{2}}{\rho_{1}} \right)^{\gamma}$
$= p\left( \frac{2}{1} \right)^{7/5} = 2.63p$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.