question_answer

A volume of a gas enclosed in a cylinder is\[1000c{{m}^{3}}\]. If the pressure on the gas is reduced slowly to of \[{\scriptstyle{}^{1}/{}_{4}}\]the original value, calculate the final volume.

Answer:

Case - 1 Initial volume \[({{V}_{1}})=1000\text{ }c{{m}^{3}}\] Initial pressure \[({{P}_{1}})=P\] Case - 2 Final volume \[({{V}_{2}})=?\] Final pressure \[({{P}_{2}})=\frac{1}{4}P\] According to Boyles law, \[{{P}_{1}}{{V}_{1}}={{P}_{2}}{{V}_{2}}\] Substituting the above values, we get, \[P\times 1000=\frac{1}{4}P\times {{V}_{2}}\] \[\Rightarrow \] \[{{V}_{2}}=(1000\times 4)\]     \[\Rightarrow \] \[{{V}_{2}}=4000\]\[c{{m}^{3}}\] Therefore, the final volume of gas\[=4000\text{ }c{{m}^{3}}.\]