Question

During the adiabatic change of ideal gas, The relation between the pressure and the density will be -

• A. $\frac{P_1}{P_2}={\left(\frac{d_2}{d_1}\right)}^{1/\gamma }$
• B. $p_1{d}_1^{\gamma }=p_2{d}_2\gamma$
• C. $p_1{d}_1^{-\gamma }=p_2{d}_2^{-\gamma }$
• D. $\frac{P_1}{P_2}={\left(\frac{d_2}{d_1}\right)}^{\gamma }$

Answer 1

The correct option is C $p_1{d}_1^{-\gamma }=p_2{d}_2^{-\gamma }$

For an adiabatic process, $P_1{V}_1^{\gamma }=P_2{V}_2^{\gamma }=cons\tan t$

Since density,

$d=\frac{m}{V}$

$V\propto \frac{1}{d}$

$P_1{\left(\frac{1}{d_1}\right)}^{\gamma }=P_2{\left(\frac{1}{d_2}\right)}^{\gamma }$

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