Question

Have you ever wondered what the pressure is under the glass bell jar when the vacuum pump is turned on? One way to measure it would be to see how a balloon changes when it is inside. At beginning of the experiment, you note that the volume of the balloon is 560ml under standard pressure. When you turned on the vacuum pump the balloon grows to 780ml. What is the pressure under the bell jar at this point?

Answer 1

Given-

$$\begin{gathered} \mathrm{T}=\mathrm{constant} \\ \mathrm{standard}\mathrm{pressure} \\ {\mathrm{P}}_1=1\mathrm{atm} \\ {\mathrm{V}}_1=560\mathrm{ml} \\ {\mathrm{V}}_2=780\mathrm{ml} \\ {\mathrm{P}}_2=? \end{gathered}$$

As the temperature is constant and the relation is between volume and pressure Boyle's law is applicable here.

According to Boyle's law-

${\mathrm{P}}_1{\mathrm{V}}_1={\mathrm{P}}_2{\mathrm{V}}_2$

Now putting all the values in the equation-

$$\begin{gathered} 1\times 560={\mathrm{P}}_2\times 780 \\ {\mathrm{P}}_2=\frac{1\times 560}{780} \\ {\mathrm{P}}_2=0.71\mathrm{atm} \end{gathered}$$

So, the final pressure will be 0.71atm.