Question

Volume of an ideal gas is to be decreased by 10% and the pressure increases 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 remains constant]
Final pressure is increased by x% of its initial value
Thus, $P_2=(P_1+\frac{x{P}_1}{100})$
Final volume is decreased by 10% of its initial value
Thus, $V_2=(V_1-\frac{10V_1}{100})\therefore p_1{V}_1=(p_1+\frac{x{p}_1}{100})(V_1-\frac{10V_1}{100})=p_1(1+0.01x)V_1(1-0.1)1=(1+0.01x)\left(0.9\right)\therefore x=\frac{(\frac{1}{0.9}-1)}{0.01}\Rightarrow x=\frac{100}{9}$