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

The correct option is B $1.4$

Volume of the gas $v=\frac{mass}{density}=\frac{m}{\rho }$ and using $(PV{)}^r=$ constant,

$\frac{P^{\prime }}{P}=\frac{V}{V^{\prime }}={\left(\frac{m\rho }{m\rho }\right)}^r={\left(\frac{{\rho }^{\prime }}{\rho }\right)}^r$

Or $128=(32{)}^r$

$\therefore r={\log }_{32}^{128}$

$\therefore r=\frac{7}{5}=1.4$