A) \[375{}^\circ C\]
B) \[402{}^\circ C\]
C) \[175{}^\circ C~\]
D) \[475{}^\circ C\]
Correct Answer: A
Solution :
Given: \[{{T}_{1}}=27+273=300K\] \[{{V}_{1}}=V\] (let) \[{{V}_{2}}=\frac{8}{27}V\] Then for adiabatic process \[{{T}_{1}}V_{1}^{\gamma -1}={{T}_{2}}V_{2}^{\gamma -1}\] or \[{{T}_{2}}={{T}_{1}}{{\left( \frac{{{V}_{1}}}{{{V}_{2}}} \right)}^{\gamma -1}}\] For monoatomic gas, \[\gamma =5/3\] So, \[{{T}_{2}}=300{{\left( \frac{V\times 27}{8V} \right)}^{\frac{5}{3}-1}}=675K\] i.e., \[{{T}_{2}}=675-273={{402}^{o}}C\] Hence, increase in temperature \[=402-{{27}^{o}}\] \[={{375}^{o}}C\]
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