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  4. 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 ‘γ’of the gas is :

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Q. 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 :

JEE MainJEE Main 2013Thermodynamics

Solution:

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 $128 = \left(32\right)^{\gamma}$
$\therefore \gamma=\frac{7}{5}=1.4$