Question

What volume of air will be expelled from a vessel containing 400 cm3 at 7°C when it is heated to 27° C at the same pressure ?

Answer 1

Given: The volume and temperature

To find: The amount of volume expelled

Solution: As the pressure is constant, we can apply Charle's law.

\(\frac{V_{1}}{T_{1}}=\frac{V_{2}}{T_{2}} \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots . .\) (i)

Now,

\(\mathrm{V}_{1}\) =initial volume \(=400 \mathrm{~cm}^{3}\)

\(\mathrm{T}_{1}\) =initial temperature \(=(273+7) \mathrm{K}=280 \mathrm{~K}\)

\(\mathrm{V}_{2}=\) final volume =unknown

\(\mathrm{T}_{2}=\) final temperature \(=(273+27)=300 \mathrm{~K}\)

Now from equation-(i)

\(\frac{400}{280}=\frac{V_{2}}{300}\)

\(V_{2}=428.6 \mathrm{~cm}^{3}\)

Hence, the volume expelled out \(=(428.6-400) \mathrm{cm}^{3}=28.6 \mathrm{~cm}^{3}\)

The volume of the air will be 28.6cm³