Question

In an adiabatic process pressure is increased by $\frac{2}{3}\%$ if $\frac{C_p}{C_v}=\frac{3}{2}$. Then the volume decrease by about

• A. $\frac{4}{9}\%$
• B. $\frac{2}{3}\%$
• C. $4\%$
• D. $\frac{9}{4}\%$

Answer 1

The correct option is A $\frac{4}{9}\%$

In an adiabatic process, $P{V}^{\gamma }=constant$

$\gamma =\frac{C_P}{C_V}=\frac{3}{2}$

Thus $P_0{V}_0^{\gamma }=P_0(1+\frac{2/3}{100})V^{\gamma }$

$⟹V=\frac{V_0}{(1+\frac{2/3}{100}{)}^{1/\gamma }}$

$=V_0(1+\frac{2/3}{100}{)}^{-2/3}$

$\approx V_0(1-\frac{4/9}{100})$

Thus, volume decreases by $\frac{4}{9}$%