Question

Volume of an ideal gas is to be decreased by 10% by increase of pressure by $x\%$ under isothermal condition. Thus, $x$ is

• A. $\frac{9}{100}$
• B. $\frac{100}{9}$
• C. $10$
• D. $\frac{1}{10}$

Answer 1

The correct option is B $\frac{100}{9}$

By Boyle's law
$P_1{V}_1=P_2{V}_2$
[$\because$ under isothermal condition, temperature remain constant]
Final pressure is increased by $x\%$ of initial value
Thus, $P_2=(P_1+\frac{x{P}_1}{100})$
Final volume is decreased by 10% of initial value
Thus, $V_2=(V_1-\frac{10V_1}{100})$
$\therefore P_1{V}_1=(P_1+\frac{x{P}_1}{100})(V_1-\frac{10V_1}{100})$
$=P_1(1+0.01x)V_1(1-0.1)$
$1=(1+0.01x)\left(0.9\right)$
$\therefore x=\frac{(\frac{1}{0.9}-1)}{0.01}$
$\Rightarrow x=\frac{100}{9}$