Step 1: Analyze the given ratio.
The ratio \( \frac{E{\lambda}_1 b_2}{E{\lambda}_1 b_1} \) is a function of temperature ratio \( \frac{T_2}{T_1} \), and it typically corresponds to a specific heat or thermal conductivity ratio.
Step 2: Conclusion.
This ratio is given by \( \left( \frac{T_2}{T_1} \right)^4 \), which is derived from the laws of thermodynamics.
Final Answer:
\[
\boxed{\left( \frac{T_2}{T_1} \right)^4}
\]