A) \[{{375}^{o}}C\]
B) \[{{402}^{o}}C\]
C) \[{{175}^{o}}C\]
D) \[{{475}^{o}}C\]
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, \[{{T}_{2}}=300{{\left( \frac{V\times 27}{8\,V} \right)}^{\frac{5}{3}-1}}=675\,K\] \[i.e.,\] \[{{T}_{2}}=675-273={{402}^{o}}C\] Hence, increase in temperature \[=402-{{27}^{o}}={{375}^{o}}C\]
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