A) 375 K
B) 450 K
C) 225 K
D) 405 K
Correct Answer: A
Solution :
For adiabatic process \[\frac{{{T}_{1}}}{{{T}_{2}}}={{\left( \frac{{{V}_{2}}}{{{V}_{1}}} \right)}^{\gamma -1}}\] \[{{T}_{2}}={{T}_{1}}{{\left( \frac{{{V}_{1}}}{{{V}_{2}}} \right)}^{\gamma -1}}\] \[=(273+27){{\left\{ \frac{V}{\frac{8}{27}V} \right\}}^{\frac{5}{3}-1}}\] \[=300{{\left\{ \frac{27}{8} \right\}}^{2/3}}\] \[=300{{\left\{ \frac{3}{2} \right\}}^{3\times \frac{2}{3}}}\] \[=300\times \frac{9}{4}=675K\] Rise in temperature \[\Delta T=675-300\] \[=375K\]
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