Question

A balloon inflated with three breaths of air has a volume of \({\rm{1}}{\rm{.7\;L}}\). At the same temperature and pressure, what is the volume of the balloon if five more same-sized breaths are added to the balloon?

Short answer

The final volume of balloon \({\rm{ = 4}}{\rm{.53\;L}}\).

Step-by-step solution

Definition of pressure

The physical force exerted on an item is known as pressure. The force applied per unit area is perpendicular to the surface of the objects.

Calculating the volume of the balloon

A balloon inflated with three breaths of air has a volume of \({\rm{1}}{\rm{.7L}}\)when kept at the same temperature and pressure.

Comparative example: (At same temperature and pressure.)

\(3{\rm{ }}breaths{\rm{ }}of{\rm{ }}air{\rm{ = 1}}{\rm{.7\;L}}\).

\(\begin{aligned}{}1{\rm{ }}breaths{\rm{ }}of{\rm{ }}air\,{\rm{ = }}\frac{{{\rm{1}}{\rm{.7}}}}{{\rm{3}}}{\rm{L}}{\rm{.}}\\{\rm{ = 0}}{\rm{.56\;L}}{\rm{.}}\end{aligned}\)

\(\begin{aligned}{}{\rm{5 }}breaths {\rm{ }} of {\rm{ }} air = 5 \times 1{\rm{ }}breaths {\rm{ }}of{\rm{ }}air\\{\rm{ = 5 \times (0}}{\rm{.56)L}}{\rm{.}}\\{\rm{ = 2}}{\rm{.83\;L}}{\rm{.}}\end{aligned}\)

Initial volume of balloon \({\rm{ = 3}}\) breaths of air

\(\begin{aligned}{}{\rm{ Final volume of balloon = (3 breaths of air ) + (5 breaths of air )}}\\{\rm{ = 1}}{\rm{.7L + 2}}{\rm{.83L}}\\{\rm{ = (1}}{\rm{.7 + 2}}{\rm{.83)L}}{\rm{.}}\\{\rm{ = 4}}{\rm{.53L}}{\rm{.}}\end{aligned}\)

Therefore, the final volume of balloon \({\rm{ = 4}}{\rm{.53\;L}}\).