A) \[5\times {{10}^{4}}J\]
B) \[6\times {{10}^{4}}J\]
C) \[7\times {{10}^{4}}J\]
D) \[3\times {{10}^{4}}J\]
Correct Answer: A
Solution :
[a] \[\text{Volume=}\frac{\text{mass}}{\text{density}}=\frac{1}{4}{{m}^{3}}\] \[\text{K}\text{.E}\text{.}=\frac{5}{2}PV=\frac{5}{2}\times 8\times {{10}^{4}}\times \frac{1}{4}=5\times {{10}^{4}}J\] Alternatively: \[\text{K}\text{.E}\text{.}=\frac{5}{2}nRT=\frac{5}{2}\frac{m}{M}RT=\frac{5}{2}\frac{m}{M}\times \frac{PM}{d}\] \[\left[ \therefore PM=dRT \right]\] \[=\frac{5}{2}\frac{mP}{d}=\frac{5}{2}\times \frac{1\times 8\times {{10}^{4}}}{4}=5\times {{10}^{4}}J\]
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