A) \[{{480}^{o}}C\]
B) \[{{275}^{o}}C\]
C) \[{{450}^{o}}C\]
D) \[{{375}^{o}}C\]
Correct Answer: D
Solution :
When a system undergoes a change under the condition that no exchange of heat takes place between system and surrounding them such a process is called an adiabatic one. The relation between temperature \[(T)\], volume \[(V)\] and ratio of specific heats \[(\gamma )\] is \[T{{V}^{\gamma -1}}=\]constant \[\therefore \] \[\frac{T'}{T}={{\left( \frac{V}{V'} \right)}^{\gamma -1}}={{\left( \frac{27}{8} \right)}^{\frac{5}{3}-1}}={{\left( \frac{27}{8} \right)}^{\frac{2}{3}}}\] \[\Rightarrow \] \[\frac{T'}{T}={{\left( \frac{3}{2} \right)}^{2}}=\frac{9}{4}\] \[\Rightarrow \] \[T'=\frac{9}{4}T=\frac{9}{4}\times (273+27)\] \[\Rightarrow \] \[T'=\frac{9}{4}\times 300=675\,\,K\]
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