• # question_answer An ideal gas at ${{27}^{o}}C$ is compressed adiabatically to $\frac{8}{27}$ of its original volume.  If $\gamma =\frac{5}{3}$,  then the rise in temperature is A) 450 K B) 375 K C) 225 K D) 405 K

 [b] $\frac{{{T}_{2}}}{{{T}_{1}}}={{\left( \frac{{{V}_{1}}}{{{V}_{2}}} \right)}^{\gamma -1}}\Rightarrow {{T}_{2}}=300\,{{\left( \frac{27}{8} \right)}^{\frac{5}{3}-1}}=300\,{{\left( \frac{27}{8} \right)}^{\frac{2}{3}}}$ $=300\,{{\left\{ {{\left( \frac{27}{8} \right)}^{1/3}} \right\}}^{2}}=800\,{{\left( \frac{3}{2} \right)}^{2}}=675K$ $\Rightarrow \ \Delta T=675-300=375\ K$