Question

The pressure and density of a diatomic gas $(\gamma =\frac{7}{5})$ change adiabatically form $(p_1,d_1)$ to $(p_2,d_2)$. If $\frac{d_2}{d_1}=32,then\frac{p_2}{p_1}$ is

• A. $\frac{1}{128}$
• B. 32
• C. 128
• D. 256

Answer 1

The correct option is C

128

${}_p{V}^{\gamma }=constant$. For a given mass of gas, $V\propto \frac{1}{d}$.
Hence
$\frac{p}{d^{\gamma }}=constant\therefore \frac{p_1}{d_1^{\gamma }}=\frac{p_2}{d_2^{\gamma }}or\frac{p_2}{p_1}={\left(\frac{d_2}{d_1}\right)}^{\gamma }=(32{)}^{\frac{7}{5}}=(2{)}^7=128$