Question

An ideal gas at atmospheric pressure is adiabatically compressed so that its density becomes $32$ times of its initial value. If the final pressure of gas is $128$ atmospheres, the value of ?$\gamma$?of the gas is :

• A. $1.5$
• B. $1.4$
• C. $1.3$
• D. $1.6$

Answer 1

Answer: (B)

$1.4$

Answer 2

Volume of the gas
$v=\frac{m}{d}$ and
using $pV^{\gamma} =$ constant
$\frac{P'}{P}=\frac{V}{V '}=\left(\frac{d '}{d}\right)^{\gamma}$
or $128 = \left(32\right)^{\gamma}$
$\therefore \gamma=\frac{7}{5}=1.4$