question_answer

A gas present in a cube of length 1 is shifted to another cube of length 21. What is the pressure of the gas in the 2nd case, if the pressure of the gas in the 1st case is P at the same temperature?

Answer:

               

\[{{1}^{st}}\] Cube	\[{{2}^{nd}}\] Cube
\[{{\ell }_{2}}=2\ell \]	\[{{\ell }_{2}}=2\ell \]
\[\Rightarrow \]\[{{V}_{1}}={{\ell }^{3}}\]	\[\Rightarrow \]\[{{V}_{2}}={{(2\ell )}^{3}}={{(81)}^{3}}\]
\[{{P}_{1}}=P\]	\[{{P}_{2}}=?\]
Temperature is constant

Temperature is constant \[\Rightarrow \] \[{{P}_{1}}{{V}_{1}}={{P}_{2}}{{V}_{2}}\] \[\Rightarrow \]\[{{P}_{2}}=\frac{P\times {{\ell }^{3}}}{8{{\ell }^{3}}}\] \[\Rightarrow \]Boyles law is applicable \[\Rightarrow \]\[P\times {{\ell }^{3}}={{P}_{2}}\times 8{{\ell }^{3}}\] \[\therefore \]\[{{P}_{2}}=\frac{P}{8}\]