Answer
$\frac{v_{rms \space i}^2}{v_{rms \space f}^2}=0.010$
Work Step by Step
As we know that;
$\frac{v_{rms \space i}^2}{v_{rms \space f}^2}=\frac{T_i}{T_f}$
We plug in the known values to obtain:
$\frac{v_{rms \space i}^2}{v_{rms \space f}^2}=\frac{273}{2.7\times 10^4}=0.010$