A) \[2700\,\,{{m}^{3}}\]
B) \[1900\,\,{{m}^{3}}\]
C) \[1700\,\,{{m}^{3}}\]
D) \[1500\,\,{{m}^{3}}\]
Correct Answer: A
Solution :
The general gas equation is \[\frac{{{p}_{1}}{{V}_{1}}}{{{T}_{1}}}=\frac{{{p}_{2}}{{V}_{2}}}{{{T}_{2}}}=\] gas constant where\[{{p}_{1}},\,\,{{V}_{1}},\,\,{{p}_{2}},\,\,{{V}_{2}}\]are pressure and volume at temperatures\[{{T}_{1}}\]and\[{{T}_{2}}\]respectively. Given\[{{V}_{1}}=1500\,\,{{m}^{3}},\,\,{{T}_{1}}=27+273=300\,\,K\] \[{{p}_{1}}=4\,\,\,atm\]. \[{{T}_{2}}=-{{3}^{o}}C=273-3=270\,\,K,\,\,{{p}_{2}}=2\,\,atm\]. \[\therefore \] \[{{V}_{2}}=\frac{{{p}_{1}}{{V}_{1}}}{{{T}_{1}}}\times \frac{{{T}_{2}}}{{{p}_{2}}}\] \[{{V}_{2}}=\frac{4\times 1500}{300}\times \frac{270}{2}\] \[{{V}_{2}}=2700\,\,{{m}^{3}}\]
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