question_answer

There is a gas in a sphere of radius 2r at a pressure P. If the same amount of gas is present in another sphere of radius r at same temperature, find its pressure:

Answer:

\[{{R}_{1}}=2r\] \[{{V}_{1}}=\frac{4}{3}\pi R_{1}^{3}\Rightarrow {{V}_{1}}=\frac{4}{3}\pi {{(2r)}^{3}}=\frac{4}{3}\pi \times 8{{r}^{3}}={{P}_{1}}=P\] \[{{R}_{2}}=r\] \[{{V}_{2}}=\frac{4}{3}\pi R_{2}^{3}\Rightarrow {{V}_{2}}=\frac{4}{3}\pi {{r}^{3}}\] \[{{P}_{2}}=?\]                  \[{{P}_{1}}{{V}_{1}}={{P}_{2}}{{V}_{2}}\] \[P\times \frac{4}{3}\pi 8{{r}^{3}}={{P}_{2}}\times \frac{4}{3}\pi {{r}^{3}}\Rightarrow {{P}_{2}}=8P\]