Question

The volume of a gas is directly proportional to its absolute temperature and inversely proportional to pressure on it. When volume is 140 ml the absolute temperature is 280°K and the pressure on it is 15 mm. If the absolute temperature is 300°K, the pressure on it is 20 mm. Find the difference in its volume.

Answer 1

$$\begin{gathered} \mathrm{Let}V,T\mathrm{and}P\mathrm{denote}\mathrm{the}\mathrm{volume},\mathrm{absolute}\mathrm{temperature}\mathrm{and}\mathrm{pressure}\mathrm{of}\mathrm{the}\mathrm{gas},\mathrm{respectively}. \\ V\alpha T\left(G\mathrm{iven}\right) \\ V\alpha \frac{1}{P}\left(G\mathrm{iven}\right) \\ \mathrm{Thus},wehave: \\ V\alpha \frac{T}{P} \\ \Rightarrow V=\frac{kT}{P}\left(k\mathrm{is}\mathrm{constant}.\right) \\ \therefore 140=\frac{k\times 280}{15}\left(V=140mL,T=280\mathrm{K}\mathrm{and}P=15\mathrm{mm}\right) \\ \Rightarrow k=\frac{140\times 15}{280} \\ \Rightarrow k=7.5 \\ \therefore V=\frac{7.5T}{P}\left(\mathrm{Equation}\mathrm{of}\mathrm{variation}\right) \\ \Rightarrow V=\frac{7.5\times 300}{20}\left(T=300°\mathrm{K}\mathrm{and}P=20\mathrm{mm}\right) \\ \Rightarrow V=112.5mL \\ \mathrm{Difference}\mathrm{in}\mathrm{volume}=\left(140-112.5\right)mL=27.5mL \end{gathered}$$