Question

A gas at pressure p is adiabatically compressed so that its density becomes twice that of initial value. Given that $\gamma =C_P/C_v=7/5$ what will be the final pressure of the gas?

• A. 2 p
• B. $\frac{7}{5}$ p
• C. 2.63 p
• D. p

Answer 1

The correct option is C 2.63 p

As $p_2{V}_2^{\gamma }=p_1{V}_1^{\gamma }$
Therefore $p_2=p_1{\left(\frac{V_1}{V_2}\right)}^{\gamma }=P_1{\left(\frac{{\rho }_2}{{\rho }_1}\right)}^{\gamma }$
$=p{\left(\frac{2}{1}\right)}^{\frac{7}{5}}=2.63p$