A) \[18{}^\circ \,C\]
B) \[887.4{}^\circ \,C\]
C) \[395.4{}^\circ \,C\]
D) \[144{}^\circ \,C\]
Correct Answer: C
Solution :
Given: Initial temperature \[({{T}_{1}})=18{}^\circ C\]\[=(273+18)=291K\]and\[{{V}_{2}}=1\text{/}8\,\,{{V}_{1}}.\] We know that for adiabatic compression, \[T{{V}^{\gamma -1}}=\text{Constant}\] or \[{{T}_{1}}{{V}_{1}}^{\gamma -1}={{T}_{2}}V_{2}^{\gamma -1}\] Therefore\[{{T}_{2}}={{T}_{1}}{{\left( \frac{{{V}_{1}}}{{{V}_{2}}} \right)}^{\gamma -1}}=291\times {{(8)}^{1.4-1}}\] \[=291\times {{(8)}^{0.4}}=291\times 2.297\] \[=668.4\,K.\] \[=395.4{}^\circ \,C\]
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