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

Hint: 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.