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\[=4000\text{ }c{{m}^{3}}.\]
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