Question

In an adiabatic compression of air, the pressure increases by 5%. The % change in volume is:

Answer 1

$\gamma$ for air $=1.4$

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

$P_1{V}_1^{\gamma }=1.05P_1{V}_2^{\gamma }$

$\frac{V_2}{V_1}=(1/1.05{)}^{1/1.4}$

$\frac{V_2}{V_1}=0.97$

$\frac{V_1-V_2}{V_1}=0.03$

Hence, percentage change in volume $=3\%$

Hence, the correct answer is $3$.