Question

Two glass bulbs A and B are connected by a very small tube having a stop cock. Bulb A had a volume of $100c{m^3}$ and contained the gas, while bulb B was empty. On opening the stop cock, the pressure fell down $40\%$. The volume of the bulb must be?
A. $75c{m^3}$
B. $125c{m^3}$
C. $150c{m^3}$
D. $250c{m^3}$

Answer 1

The product of pressure of A and volume of A is equal to the product of final volume and pressure of the whole system. This is in accordance with Boyle's law. The final volume is the sum of volume of A and B. As the pressure decreases to 40%, so the final pressure will be 40% of initial pressure.

Complete Step by step answer:
Two glass bulbs named as A and B are connected by a small tube with a stop cock attached to it. Bulb A is filled with the gas and has a volume of $100c{m^3}$ and bulb B is empty. The purpose of the stop cock is to prevent the movement of gas from bulb A to bulb B.

Now, the stop cock is opened and the pressure falls down to $40\%$ of initial pressure. Let the initial volume be represented by ${V_i} = 100c{m^3}$, initial pressure be ${P_i}$, final volume be ${V_f} = 100 + {V_2}$ (since the stop cock is opened, so the final volume will be the sum of total volume of bulb A and B) and final pressure be ${P_f} = 40\%$ of ${P_i}$ i.e., $\dfrac{{40{P_i}}}{{100}}$. ${V_2}$ denotes the volume of glass bulb B.

According to Boyle’s law, the product of pressure $\left( P \right)$ and volume $\left( V \right)$ is constant $\left( k \right)$ at constant temperature i.e., $PV = k$. So, we can write ${P_i}{V_i} = k$ and ${P_f}{V_f} = k$. Thus, ${P_i}{V_i} = {P_f}{V_f}$
$\Rightarrow {P_i} \times 100 = \left( {\dfrac{{40{P_i}}}{{100}}} \right) \times \left( {100 + \Rightarrow {V_2}} \right)$
$\Rightarrow 100{P_i} = \left( {\dfrac{{2{P_i}}}{5}} \right) \times \left( {100 + {V_2}} \right)$
$\Rightarrow 100 \times \dfrac{5}{2} = 100 + {V_2}$
$\Rightarrow 250 = 100 + {V_2}$
$\Rightarrow {V_2} = 250 - 100$
$\Rightarrow {V_2} = 150c{m^3}$

Therefore, option C is correct.

Note: Remember that the initial volume will be the volume of glass bulb A only as glass bulb B was initially empty and final volume will be the sum of volume of A and B as the gas flows from bulb A to bulb B after opening the stop cock and also memorize the Boyle’s law as it gives us the main idea to solve this problem.