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 :

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

Tardigrade Admin · Accepted Answer

Volume of the gas v=(m/d) and using pV&gamma; = constant (P'/P)=(V/V ')=((d '/d))&gamma; or 128 = (32)&gamma; ∴ &gamma;=(7/5)=1.4

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 ‘ $γ$ ’of the gas is :

$1.5$

$1.4$

$1.3$

$1.6$

Volume of the gas
$v = \frac{m}{d}$ and
using $p V^{γ} =$ constant
$\frac{P ^{'}}{P} = \frac{V}{V ^{'}} = (\frac{d ^{'}}{d})^{γ}$
or $128 = (32)^{γ}$
$∴ γ = \frac{7}{5} = 1.4$

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 ‘γ’of the gas is :

1.5

1.4

1.3

1.6