Question

An ideal gas at pressure P is adiabatically compressed so that its density becomes n times the initial value. The final pressure of the gas will be $(\gamma =\frac{C_p}{C_v})$

• A. $n^{\gamma }P$
• B. $(n-\gamma )P$
• C. $n(\gamma -1)P$
• D. $n(1-\gamma )P$

Answer 1

Answer: (A)

$n^{\gamma }P$

Given,

$P_1=P$

$P_2=?$

${\rho }_1=\rho$

${\rho }_2=n\rho$

For adiabatic compression,

$P{V}^{\gamma }=constant$

$P{\left(\frac{m}{\rho }\right)}^{\gamma }=constant$

value of $m=constant$

$P{\rho }^{-\gamma }=constant$

$P_1{\rho }_1^{-\gamma }=P_2{\rho }_2^{-\gamma }$

$P{\rho }^{-\gamma }=P_2{n}^{-\gamma }{\rho }^{-\gamma }$

$P_2=n^{\gamma }P$