Question

A rubber balloon contains some marbles each occupying a volume of $10\text{mL}$. A gas is filled in the balloon at a pressure of $2\text{atm}$ and the total volume of the balloon is $1\text{litre}$ in this condition. If the external pressure is increased to $4\text{atm}$ the volume of the balloon becomes $625\text{mL}$. Find the number of marbles present in the balloon.

• A. 10
• B. 15
• C. 25
• D. 50

Answer 1

The correct option is C 25

Let the total no. of marbles be $=n$
so, total volume of all marbles = $10n\text{mL}$
volume of balloon earlier $=1000\text{mL}$
and final $=625\text{mL}$
Now for the gas inside the balloon, the temperature and amount of the gas is constant, hence Boyle's law can be applied
$P_1{V}_1=P_2{V}_2$
$4\times (625-10n)=2\times (1000-10n)$
$625\times 4-2000=-20n+40n$
$625\times 4-2000=20n$
$\frac{625\times 4-2000}{20}=n,orn=25$
Thus, the number of marbles is 25.