Question

The pressure and density of a diatomic gas $(\gamma =7/5)$ change adiabatically from (P,d) to (P',d') if $\frac{d^{\prime }}{d}=32$ then $\frac{P^{\prime }}{P}$ should be

• A. $\frac{1}{128}$
• B. 32
• C. 128
• D. None of the above

Answer 1

The correct option is C 128

Volume of the gas $V=\frac{m}{d}$ where , m is the mass and d is the density of the gas. and using $P{V}^{\gamma }$ = constant we get
$\frac{P^{\prime }}{P}={\left(\frac{V}{V^{\prime }}\right)}^{\gamma }={\left(\frac{d^{\prime }}{d}\right)}^{\gamma }=(32{)}^{\frac{7}{5}}=128$