Question

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

• A. 1/128
• B. 32
• C. 128
• D. None of the above

Answer 1

The correct option is C

128

Volume of the gas $V=\frac{m}{d}$ and using $P{V}^{\gamma }=constant$

We get $\frac{P^{\prime }}{P}={\left(\frac{V}{V}\right)}^{\gamma }={\left(\frac{d^{\prime }}{d}\right)}^{\gamma }=(32{)}^{\frac{7}{5}}=128$