A) \[-235{}^\circ \,C\]
B) \[-182{}^\circ \,C\]
C) \[-91{}^\circ \,C\]
D) \[0{}^\circ \,C\]
Correct Answer: B
Solution :
\[For adiabatic process\,\,T{{V}^{\gamma -1}} = constant\] \[\Rightarrow \,\,\,\frac{{{T}_{2}}}{{{T}_{1}}}\,\,=\,\,{{\left( \frac{{{V}_{1}}}{{{V}_{2}}} \right)}^{\gamma -1}}\,\,\,\,\Rightarrow \,\,{{T}_{2}}\,\,=\,\,{{\left( \frac{{{V}_{1}}}{{{V}_{2}}} \right)}^{\gamma -1}}\,\,\times \,\,{{T}_{1}}\] \[\Rightarrow \,\,\,\,{{T}_{2}}={{\left( \frac{1}{81} \right)}^{1.25-1}}\,\times 273\,\,=\,\,{{\left( \frac{1}{81} \right)}^{0.25}}\,\,\times \,\,273\] \[=\,\frac{273}{3}\,\,=\,\,91\,K\,\,\,\to \,\,-182{}^\circ \,C\,\]
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