Question

For adiabatic expansion of perfect monoatomic gas , when voulme increases by $24\%$ ,what is the percentage decrease in pressure ?

• A. $24\%$
• B. $30\%$
• C. $48\%$
• D. $71\%$

Answer 1

Answer: (B)

$30\%$

In adiabatic process $p_2{V}_2^{\gamma }=p_1{V}_1^{\gamma }$
$p_2=p_1(\frac{V_1}{V_2}{)}^{\gamma }$
$p_2=(\frac{100}{124}{)}^{5/3}{p}_1$
$p_2=0.6985p_1$
$\%$ decrease in pressure
$=\frac{p_1-p_2}{p_1}\times 100\%$
$=\frac{p_1-0.6985p_1}{p_1}\times 100\%$
$=\frac{0.3015p_1}{p_1}\times 100\%$
$=30.15\%=30\%$