Question

In an adiabatic expansion of air, the volume increases by $5\%$ . The corresponding percentage change in pressure will be $\left[{\left(1.05\right)}^{\frac{7}{5}}=1.07\right]$

• A. $7\%$
• B. $6\%$
• C. $4\%$
• D. $3\%$

Answer 1

Answer: (A)

$P_1{V}_1^{\gamma }=P_2{V}_2^{\gamma }\left(\gamma =\frac{7}{5}\right),V_2=1.05V_1$
$P_1{V}_1^{\gamma }=P_2{\left(1.05V_1\right)}^{\gamma }$
$P_2=\frac{P_1}{{\left(1.05\right)}^{\gamma }}$
So % change $\frac{P_2-P_1}{P_1}\times 100$
$=\frac{\frac{P_1}{{\left(1.05\right)}^{\gamma }}}{P_1}\times 100=\frac{1-{\left(1.05\right)}^{\gamma }}{{\left(1.05\right)}^{\gamma }}\times 100=7\%$