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 $40\mathrm{\%}$. 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 $40\mathrm{\%}$ 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 $P_f=40\mathrm{\%}$ of $P_i$ i.e., ${\displaystyle \frac{40P_i}{100}}$. $V_2$ 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, $P_i{V}_i=P_f{V}_f$
 $\Rightarrow P_i\times 100=\left({\displaystyle \frac{40P_i}{100}}\right)\times \left(100+\Rightarrow V_2\right)$
 $\Rightarrow 100P_i=\left({\displaystyle \frac{2P_i}{5}}\right)\times \left(100+V_2\right)$
 $\Rightarrow 100\times {\displaystyle \frac{5}{2}}=100+V_2$
 $\Rightarrow 250=100+V_2$
 $\Rightarrow V_2=250-100$
 $\Rightarrow V_2=150c{m}^3$

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.