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 \[T{{V}^{\gamma -1}}=\text{constant}\] \[\therefore \] \[\frac{T}{T}={{\left( \frac{V}{V} \right)}^{\gamma -1}}={{\left( \frac{27}{8} \right)}^{\frac{5}{3}-1}}={{\left( \frac{27}{8} \right)}^{\frac{2}{3}}}\] \[\Rightarrow \] \[\frac{T}{T}={{\left( \frac{3}{2} \right)}^{2}}=\frac{9}{4}\] \[\Rightarrow \] \[T=\frac{9}{4}T=\frac{9}{4}\times (273+27)\] \[\Rightarrow \] \[T=\frac{9}{4}\times 300=675\,K\] \[\therefore \]\[\Delta \Tau =T-T=675-3000=375\,K=375{{\,}^{o}}C\]
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