Question

In the figures given below, a doll is entrapped within a piston and cylinder containing gas. The initial and final conditions are shown as Fig. I and Fig. II respectively. The volume of doll is:

• A. $100\text{mL}$
• B. $\frac{15000}{17}\text{mL}$
• C. $\frac{1000}{3}\text{mL}$
• D. $\frac{1000}{15}\text{mL}$

Answer 1

The correct option is C $\frac{1000}{3}\text{mL}$

According to Boyle's law:
$P_1{V}_1=P_2{V}_2$
i.e $\frac{P_1}{P_2}=\frac{V_2}{V_1}$
$\Rightarrow$ $\frac{10}{7}=\frac{1000-V_{doll}}{800-V_{doll}}$
$\Rightarrow$ $8000-10V_{doll}=7000-7V_{doll}$
$\Rightarrow$ $3V_{doll}=1000\text{mL}$
So, $V_{doll}=\frac{1000}{3}\text{mL}$