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)

$P_{1}V_{1}^{\gamma }=P_{2}V_{2}^{\gamma }\left(\gamma = \frac{7}{5}\right), \, V_{2}=1.05 \, V_{1}$
$P_{1}V_{1}^{\gamma }=P_{2}\left(1.05 \, V_{1}\right)^{\gamma }$
$P_{2}=\frac{P_{1}}{\left(1.05\right)^{\gamma }}$
So % change $\frac{P_{2} - P_{1}}{P_{1}}\times 100$
$=\frac{\frac{P_{1}}{\left(1.05\right)^{\gamma }}}{P_{1}}\times 100=\frac{1 - \left(1.05\right)^{\gamma }}{\left(1.05\right)^{\gamma }}\times 100=7\%$