A) \[405\,\,K\]
B) \[225\,\,K\]
C) \[375\,\,K\]
D) \[450\,\,K\]
Correct Answer: C
Solution :
When a system undergoes a change under the condition that no exchange of heat takes place between systems and surrounding then, such a process is called an adiabatic one. The relation between temperature\[\left( T \right)\], volume \[\left( V \right)\] and ratio of specific heats \[\left( \gamma \right)\] is \[T{{V}^{\gamma -1}}=\]Constant \[\therefore \] \[\frac{T'}{T}={{\left( \frac{V}{V'} \right)}^{\gamma -1}}={{\left( \frac{27}{8} \right)}^{\frac{5}{3}-1}}={{\left( \frac{27}{8} \right)}^{\frac{2}{3}}}\] \[\Rightarrow \] \[\frac{T'}{T}={{\left( \frac{27}{8} \right)}^{2/3}}={{\left( \frac{3}{2} \right)}^{2}}=\frac{9}{4}\] \[\Rightarrow \] \[T'=T\times \frac{9}{4}=\left( 273+27 \right)\times \frac{9}{4}\] \[=300\times \frac{9}{4}=675\,K\] \[\therefore \,\Delta T=T'-T=\left( 675-300 \right)K=375\,K\]
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